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authorNorbert Preining <norbert@preining.info>2023-03-14 03:01:36 +0000
committerNorbert Preining <norbert@preining.info>2023-03-14 03:01:36 +0000
commit2ba976b06ff8c59f0eec2151c5afb7671a35671e (patch)
tree4bcddcd2b5d5460c8bafe11a5fb89cd75ea6dca1 /macros/latex/contrib/principia
parente3c18c7072eebabaa706008b7fa42c73ec2ff83e (diff)
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-rw-r--r--macros/latex/contrib/principia/principia.sty594
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+\documentclass[12pt,openany,leqno,twocolumn]{book}
+%Licensed under LaTeX Project Public License 1.3c.
+%This is a list of definitions for use with the principia package, Version 2.0.
+%Copyright Landon D. C. Elkind, 2021 (https://landonelkind.com/contact/).
+
+\usepackage{newtxtext}
+%\usepackage{mathptmx}
+
+%Principia package requirements
+\usepackage{pifont} %This loads the eight-pointed asterisk.
+\usepackage{amssymb} %This loads the relation domain and converse domain limitation symbols.
+\usepackage{graphicx} %This loads commands that flip iota for definite descriptions, Lambda for the universal class, and so on. The (superseded) graphics package should also work here, but is not recommended.
+%\usepackage{amssymb}
+\usepackage{amsmath} %This loads the circumflex, substitution into theorems, \text{}, \mathbf{}, \boldsymbol{}, \overleftarrow{}, \overrightarrow{}, etc.
+
+\usepackage{fullpage}
+\usepackage{perpage}
+\usepackage[T1]{fontenc}
+\usepackage[utf8]{inputenc}
+\usepackage{mathrsfs}
+\usepackage[hidelinks,pdfencoding=unicode]{hyperref}
+\usepackage{enumitem}
+\usepackage{moreenum}
+\usepackage[normalem]{ulem}
+\usepackage[perpage,symbol]{footmisc}
+\usepackage{setspace}
+
+%Volume I
+%Mathematical logic
+%The theory of deduction
+%Meta-logical symbols
+\newcommand{\pmfd}{\begin{center} \rule{5cm}{.5pt} \end{center}} %Dividing line between introductory remarks in a starred number and the formal deductions.
+\newcommand{\pmdem}{\textit{Dem}.} %This notation begins a proof.
+\newcommand{\pmdemi}{\indent \pmdem} %This idents the notation that begins a proof.
+\newcommand{\pmhp}{\text{Hp}} %This typesets Hp (short for antecedent), which occurs at the beginning of a proof.
+\newcommand{\pmprop}{\text{Prop}} %This occurs at the end of a proof.
+\newcommand{\pmithm}{\pmimp\;\pmthm} %This occurs when a meta-theoretic implication is asserted.
+\newcommand{\pmbr}[1]{\bigg \lbrack \normalsize #1 \bigg \rbrack} %These are larger brackets for substitution.
+\newcommand{\pmsub}[2]{\bigg \lbrack \small \begin{array}{c} #1 \\ \hline #2 \end{array} \bigg \rbrack} %This is the substitution command.
+\newcommand{\pmsubb}[4]{\bigg \lbrack \small \begin{array}{c c} #1, & #3 \\ \hline #2, & #4 \end{array} \bigg \rbrack} %This is the substitution command.
+\newcommand{\pmsubbb}[6]{\bigg \lbrack \small \begin{array}{c c c} #1, & #3, & #5 \\ \hline #2, & #4, & #6 \end{array} \bigg \rbrack} %This is the substitution command.
+\newcommand{\pmsubbbb}[8]{\bigg \lbrack \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array} \bigg \rbrack} %This is the substitution command.
+\newcommand{\pmSub}[3]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array} \bigg \rbrack} %This is the substitution command.
+\newcommand{\pmSubb}[5]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array} \bigg \rbrack} %This is the substitution command.
+\newcommand{\pmSubbb}[7]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array} \bigg \rbrack} %This is the substitution command.
+\newcommand{\pmSubbbb}[9]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array} \bigg \rbrack} %This is the substitution command.
+\newcommand{\pmsUb}[2]{\small \begin{array}{c} #1 \\ \hline #2 \end{array}} %This is the substitution command.
+\newcommand{\pmsUbb}[4]{\small \begin{array}{c c} #1, & #3 \\ \hline #2, & #4 \end{array}} %This is the substitution command.
+\newcommand{\pmsUbbb}[6]{\small \begin{array}{c c c} #1, & #3, & #5 \\ \hline #2, & #4, & #6 \end{array}} %This is the substitution command.
+\newcommand{\pmsUbbbb}[8]{\small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}} %This is the substitution command.
+\newcommand{\pmSUb}[3]{\normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array}} %This is the substitution command.
+\newcommand{\pmSUbb}[5]{\normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array}} %This is the substitution command.
+\newcommand{\pmSUbbb}[7]{\normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array}} %This is the substitution command.
+\newcommand{\pmSUbbbb}[9]{\normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}} %This is the substitution command.
+\newcommand{\pmthm}{\mathpunct{\text{\scalebox{.5}[1]{$\boldsymbol\vdash$}}}} %This is the theorem sign.
+\newcommand{\pmast}{\text{\resizebox{!}{.75\height}{\ding{107}}}} %This is the sign introducing a theorem number.
+\newcommand{\pmcdot}{\text{\raisebox{.05cm}{$\boldsymbol{\cdot}$}}} %This is a sign introducing a theorem sub-number.
+\newcommand{\pmiddf}{\mathbin{=}}
+\newcommand{\pmdf}{\quad \text{Df}}
+\newcommand{\pmpp}{\quad \text{Pp}}
+
+%Square dots for scope, defined for up to six dots
+\newcommand{\pmdot}{\mathrel{\hbox{\rule{.3ex}{.3ex}}}}
+\newcommand{\pmdott}{\mathrel{\overset{\pmdot}{\pmdot}}}
+\newcommand{\pmdottt}{\pmdott\hspace{.1em}\pmdot}
+\newcommand{\pmdotttt}{\pmdott\hspace{.1em}\pmdott}
+\newcommand{\pmdottttt}{\pmdott\hspace{.1em}\pmdott\hspace{.1em}\pmdot}
+\newcommand{\pmdotttttt}{\pmdott\hspace{.1em}\pmdott\hspace{.1em}\pmdott}
+
+%Logical connectives
+\newcommand{\pmnot}{\mathord{\ooalign{$\boldsymbol{\sim}\mkern.5mu$\hidewidth\cr$\boldsymbol{\sim}$\cr\hidewidth$\mkern.5mu\boldsymbol{\sim}$}}}
+\newcommand{\pmor}{\mathbin{\ooalign{$\boldsymbol{\vee}\mkern.5mu$\hidewidth\cr$\boldsymbol{\vee}$\cr\hidewidth$\mkern.5mu\boldsymbol{\vee}$}}}
+\newcommand{\pmimp}{\mathbin{\ooalign{$\boldsymbol{\supset}\mkern.5mu$\hidewidth\cr$\boldsymbol{\supset}$\cr\hidewidth$\mkern.5mu\boldsymbol{\supset}$}}} %1.01
+\newcommand{\pmand}{\mathrel{\hbox{\rule{.3ex}{.3ex}}}} %3.01
+\newcommand{\pmandd}{\overset{\pmand}{\pmand}}
+\newcommand{\pmanddd}{\pmandd\hspace{.1em}\pmand}
+\newcommand{\pmandddd}{\pmandd\hspace{.1em}\pmandd}
+\newcommand{\pmanddddd}{\pmandd\hspace{.1em}\pmandd\hspace{.1em}\pmand}
+\newcommand{\pmandddddd}{\pmandd\hspace{.1em}\pmandd\hspace{.1em}\pmandd}
+\newcommand{\pmprod}{\mathbin{\ooalign{$\boldsymbol{\wedge}\mkern.5mu$\hidewidth\cr$\boldsymbol{\wedge}$\cr\hidewidth$\mkern.5mu\boldsymbol{\wedge}$}}} %Not in Principia, but added here as a dual of its symbol for disjunction.
+\newcommand{\pmiff}{\mathbin{\ooalign{$\boldsymbol{\equiv}\mkern.5mu$\hidewidth\cr$\boldsymbol{\equiv}$\cr\hidewidth$\mkern.5mu\boldsymbol{\equiv}$}}} %4.01
+
+%The theory of apparent variables
+\newcommand{\pmall}[1]{(#1)}
+\newcommand{\pmsome}[1]{(\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}#1)} %10.01
+\newcommand{\pmSome}{\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}}
+
+%Additional defined logic signs
+\newcommand{\pmhat}[1]{\mathbf{\hat{\text{$#1$}}}}
+\newcommand{\pmbreve}[1]{\mathbf{\breve{\text{$#1$}}}}
+\newcommand{\pmcirc}[1]{\mathbf{\dot{\text{$#1$}}}}
+\newcommand{\pmpf}[2]{#1#2} %for propositional functions of one variable
+\newcommand{\pmpff}[3]{#1(#2, #3)} %for propositional functions of two variables
+\newcommand{\pmpfff}[4]{#1(#2, #3, #4)} %for propositional functions of three variables
+\newcommand{\pmshr}{\textbf{!}} %*12.1 and *12.11, used for predicative propositional functions
+\newcommand{\pmpred}[2]{#1\pmshr#2} %for predicates (``predicative functions'') of one variable
+\newcommand{\pmpredd}[3]{#1\pmshr(#2, #3)} %for predicates (``predicative functions'') of two variables
+\newcommand{\pmpreddd}[4]{#1\pmshr(#2, #3, #4)} %for predicates (``predicative functions'') of three variables
+\newcommand{\pmnid}{\mathrel{\ooalign{$=$\cr\hidewidth\footnotesize\rotatebox[origin=c]{210}{\textbf{/}}\hidewidth\cr}}} %*13.02
+\newcommand{\pmiota}{\ooalign{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}\cr\hidewidth\raisebox{.0125em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.025em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.0375em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.05em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}}} %the rotated Greek iota used in definite descriptions
+\newcommand{\pmdsc}[1]{(\pmiota#1)} %*14.01
+\newcommand{\pmDsc}{\pmiota}
+\newcommand{\pmexists}{\textbf{E}\hspace{.1em}\pmshr} %*14.02
+
+%Classes and relations
+%Class signs
+\newcommand{\pmcls}[2]{\pmhat{#1}(#2)} %20.01
+\newcommand{\pmcin}{\mathop{\boldsymbol{\epsilon}}} %20.02
+\newcommand{\pmCls}{\text{Cls}} %20.03
+\newcommand{\pmClsn}[1]{\text{Cls}^{#1}}
+\newcommand{\pmcinn}{\pmnot\pmcin} %20.06
+\newcommand{\pmcinc}{\mathop{\ooalign{$\boldsymbol{\subset}$\cr\hidewidth$\hspace{.1em}\boldsymbol{\subset}$\cr\hidewidth$\hspace{.15em}\boldsymbol{\subset}$\cr\hidewidth$\hspace{.2em}\boldsymbol{\subset}$}}} %22.01
+\newcommand{\pmccap}{\mathop{\ooalign{\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.1em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.2em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.3em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.4em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.5em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.6em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}}}} %22.02
+\newcommand{\pmccup}{\mathop{\ooalign{\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.1em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.2em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.3em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.4em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.5em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.6em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}}}} %22.03
+\newcommand{\pmccmp}[1]{\boldsymbol{-}#1} %22.04
+\newcommand{\pmcmin}[2]{#1\boldsymbol{-}#2} %22.05
+\newcommand{\pmcuni}{\text{\rotatebox[origin=c]{180}{$\Lambda$}}} %24.01
+\newcommand{\pmcnull}{\mathrm{\Lambda}} %24.02
+\newcommand{\pmcexists}{\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}\hspace{-.1em}\mathop{\pmshr}} %24.03
+
+%Relation signs
+\newcommand{\pmrel}[3]{\pmhat{#1}\pmhat{#2}#3} %21.01
+\newcommand{\pmrele}[5]{#1\{\pmhat{#2}\pmhat{#3}#4(#2, #3)\}#5} %21.02
+\newcommand{\pmrelep}[3]{#1\{#2\}#3} %21.08, 21.081, 21.082, etc.
+\newcommand{\pmrcmp}[1]{\ooalign{$\hidewidth\raisebox{.25em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\mathbf{\pmccmp}$}#1} %23.04
+\newcommand{\pmrmin}[2]{#1\mathrel{\ooalign{$\hidewidth\raisebox{.25em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\mathbf{\pmccmp}$}}#2} %23.05
+\newcommand{\pmruni}{\pmcirc{\text{\rotatebox[origin=c]{180}{$\Lambda$}}}} %25.01
+\newcommand{\pmrnull}{\pmcirc{\mathrm{\Lambda}}} %25.02
+\newcommand{\pmrexists}{\pmcirc{\mathop{\text{\raisebox{.5em}{\rotatebox{180}{E}}}}}\mathop{\pmshr}} %25.03
+\newcommand{\pmrinc}{\mathrel{\ooalign{$\hidewidth\boldsymbol{\cdot}\hidewidth$\cr$\mathbf{\pmcinc}$}}} %23.01
+\newcommand{\pmrcap}{\mathrel{\ooalign{$\hidewidth\raisebox{.3em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\mathbf{\pmccap}$}}} %23.02
+\newcommand{\pmrcup}{\mathrel{\ooalign{$\hidewidth\raisebox{.1em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\mathbf{\pmccup}$}}} %23.03
+
+%Logic of Relations
+\newcommand{\pmdscf}[2]{#1\textbf{`}#2} %30.01
+\newcommand{\pmcnv}[1]{\text{Cnv}\textbf{`}#1} %31.01
+\newcommand{\pmCnv}{\text{Cnv}}
+\newcommand{\pmcrel}[1]{\pmbreve{#1}} %31.02
+\newcommand{\pmrrf}[2]{\overset{\boldsymbol{\rightarrow}}{#1\textbf{`}}#2} %32.01
+\newcommand{\pmRrf}[1]{\overset{\boldsymbol{\rightarrow}}{#1}}
+\newcommand{\pmrrl}[2]{\overset{\boldsymbol{\leftarrow}}{#1\textbf{`}}#2} %32.02
+\newcommand{\pmRrl}[1]{\overset{\boldsymbol{\leftarrow}}{#1}}
+\newcommand{\pmsg}[1]{\text{sg}\textbf{`}#1} %32.03
+\newcommand{\pmSg}{\text{sg}}
+\newcommand{\pmgs}[1]{\text{gs}\textbf{`}#1} %32.04
+\newcommand{\pmGs}{\text{gs}}
+\newcommand{\pmdm}[1]{\text{D}\textbf{`}#1} %33.01
+\newcommand{\pmDm}{\text{D}}
+\newcommand{\pmcdm}[1]{\text{\rotatebox[origin=c]{180}{D}}\textbf{`}#1} %33.02
+\newcommand{\pmCdm}{\text{\rotatebox[origin=c]{180}{D}}}
+\newcommand{\pmcmp}[1]{C\textbf{`}#1} %33.03
+\newcommand{\pmCmp}{C}
+\newcommand{\pmfld}[1]{F\textbf{`}#1} %33.04
+\newcommand{\pmFld}{F}
+\newcommand{\pmrprd}[2]{{#1}\mathop{|}{#2}} %34.01
+\newcommand{\pmRprd}{\mathop{|}}
+\newcommand{\pmrprdn}[2]{#1^{#2}} %34.02, 34.03, etc.
+\newcommand{\pmrld}[2]{#1 \boldsymbol{\upharpoonleft} #2} %35.01
+\newcommand{\pmrlcd}[2]{#1 \boldsymbol{\upharpoonright} #2} %35.02
+\newcommand{\pmrlf}[3]{#1 \boldsymbol{\upharpoonleft} #2 \boldsymbol{\upharpoonright} #3} %35.03
+\newcommand{\pmrl}[2]{#1 \boldsymbol{\uparrow} #2} %35.04
+\newcommand{\pmrlF}[2]{#1 \mathbin{\ooalign{$\upharpoonright$\cr\hidewidth\rotatebox[origin=c]{180}{\text{$\upharpoonleft$}}\hidewidth\cr}} #2} %36.01
+\newcommand{\pmdscff}[2]{#1\textbf{`}\textbf{`}#2} %37.01
+\newcommand{\pmdscfr}[2]{#1_{\pmcin}\textbf{`}#2} %37.02
+\newcommand{\pmdscfR}[1]{#1_{\pmcin}}
+\newcommand{\pmdscfcr}[2]{\pmbreve{#1}_{\pmcin}\textbf{`}#2} %37.03
+\newcommand{\pmdscfcR}[1]{\pmbreve{#1}_{\pmcin}}
+\newcommand{\pmdscfff}[2]{#1\textbf{`}\textbf{`}\textbf{`}#2} %37.04
+\newcommand{\pmdscfe}[2]{\mathop{\text{E}}\mathop{\pmshr\pmshr}\pmdscff{#1}{#2}} %37.05
+\newcommand{\Female}{{\usefont{U}{mvs}{m}{n}\symbol{126}}} %from the Marvosym package
+\newcommand{\pmop}{\mathop{\text{\Female}}} %38.01, 38.02
+\newcommand{\pmopc}[2]{#1 \mathop{\underset{\textbf{''}}{\text{\Female}}} #2} %38.03
+
+%Products and sums of classes of classes or relations
+\newcommand{\pmccsum}[1]{p\textbf{`}#1} %40.01
+\newcommand{\pmccprd}[1]{s\textbf{`}#1} %40.02
+\newcommand{\pmcrsum}[1]{\pmcirc{p}\textbf{`}#1} %41.01
+\newcommand{\pmcrprd}[1]{\pmcirc{s}\textbf{`}#1} %41.02
+\newcommand{\pmrprdd}[2]{{#1}\mathop{||}{#2}} %43.01
+\newcommand{\pmRprdd}{\mathop{||}}
+
+%Prolegomena to Cardinal Arithmetic
+%Unit Classes and Couples
+%Identity and Diversity
+\newcommand{\pmrid}{I} %50.01
+\newcommand{\pmrdiv}{J} %50.02
+\newcommand{\pmcunit}[1]{\iota\textbf{`}#1} %51.01
+\newcommand{\pmcUnit}{\iota}
+\newcommand{\pmcunits}[1]{\pmbreve{\iota}\textbf{`}#1} %52.01
+
+%Cardinal numbers
+\newcommand{\pmcn}[1]{#1} %52.01, 54.01, 54.02, etc.
+
+%Ordinal numbers
+\newcommand{\pmoc}[2]{#1 \boldsymbol{\downarrow} #2} %55.01, 55.02, etc.
+\newcommand{\pmdn}[1]{\pmcirc{#1}} %56.01
+\newcommand{\pmorn}[1]{#1_r} %56.02, 56.03, etc.
+
+%Sub-classes, Sub-relations, and Relative Types
+%Sub-classes
+\newcommand{\pmscl}[1]{\text{Cl}\textbf{`}#1} %60.01
+\newcommand{\pmsCl}{\text{Cl}}
+\newcommand{\pmscle}[1]{\text{Cl ex}\textbf{`}#1} %60.02
+\newcommand{\pmsCle}{\text{Cl ex}}
+\newcommand{\pmscls}[1]{\text{Cls}\textbf{`}#1} %60.03
+\newcommand{\pmsrl}[1]{\text{Rl}\textbf{`}#1} %61.01
+\newcommand{\pmsRl}{\text{Rl}}
+\newcommand{\pmsrle}[1]{\text{Rl ex}\textbf{`}#1} %61.02
+\newcommand{\pmsRle}{\text{Rl ex}}
+\newcommand{\pmsrel}[1]{\text{Rel}\textbf{`}#1} %61.03
+\newcommand{\pmRel}{\text{Rel}}
+\newcommand{\pmReln}[1]{\text{Rel}^{#1}} %61.04
+\newcommand{\pmrin}{\mathop{\boldsymbol{\epsilon}}} %62.01
+
+%Relative type symbols
+\newcommand{\pmrt}[1]{t\textbf{`}#1} %63.01
+\newcommand{\pmrti}[2]{t^{#1}\textbf{`}#2} %63.011
+\newcommand{\pmrtc}[2]{t_{#1}\textbf{`}#2} %63.02, 63.03, etc.
+\newcommand{\pmrtri}[2]{t^{#1}\textbf{`}#2} %63.04
+\newcommand{\pmrtrc}[2]{t_{#1}\textbf{`}#2} %64.02, 64.021, 64.022, etc.
+\newcommand{\pmrtrci}[3]{t_{#1}^{\text{ }#2}\textbf{`}#3} %64.03, 64.031, etc.
+\newcommand{\pmrtric}[3]{{}^{#1}t_{#2}\textbf{`}#3} %64.04, 64.041, etc.
+\newcommand{\pmrtdi}[2]{#1_{#2}} %65.01
+\newcommand{\pmrtdc}[2]{#1(#2)} %65.02
+\newcommand{\pmrtdri}[2]{#1_{#2}} %65.03
+\newcommand{\pmrtdrc}[2]{#1(#2)} %65.04
+
+%One-many, Many-one, and One-one relations
+%Similarity relation signs
+\newcommand{\pmrdc}[2]{#1\boldsymbol{\to}#2} %70.01
+\newcommand{\pmsmbar}{\mathrel{\overline{\text{sm}}}} %73.01
+\newcommand{\pmsm}{\mathrel{\text{sm}}} %73.02
+\newcommand{\pmSM}{\text{sm}}
+\newcommand{\pmsmarr}{\overrightarrow{{\pmsm}}}
+\newcommand{\pmonemany}{1\boldsymbol{\to}\pmCls}
+\newcommand{\pmmanyone}{\pmCls\boldsymbol{\to}1}
+\newcommand{\pmoneone}{1\boldsymbol{\to}1}
+
+%Selections
+\newcommand{\pmselp}[1]{P_{\small\Delta}\mathbf{`}#1} %80.01
+\newcommand{\pmSelp}{P_{\Delta}}
+\newcommand{\pmsele}[1]{\pmcin_{\small\Delta}\mathbf{`}#1}
+\newcommand{\pmSele}{\pmcin_{\Delta}}
+\newcommand{\pmself}[1]{F_{\small\Delta}\mathbf{`}#1}
+\newcommand{\pmSelf}{F_{\Delta}}
+\newcommand{\pmexc}{\text{Cls}^2 \mathop{\text{excl}}} %84.01
+\newcommand{\pmexcc}[1]{\text{Cl} \mathop{\text{excl}}\textbf{`}#1} %84.02
+\newcommand{\pmex}{\text{Cls excl}}
+\newcommand{\pmexcn}{\text{Cls} \mathop{\text{ex}^2} \mathop{\text{excl}}} %84.03
+\newcommand{\pmselc}[2]{#1 \mathrel{\ooalign{\rotatebox[origin=c]{270}{$\mathbf{\mapsto}$}}} #2}
+\newcommand{\pmmultr}{\mathop{\text{Rel}} \mathop{\text{Mult}}} %88.01
+\newcommand{\pmmultc}{\mathop{\text{Cls}^2} \mathop{\text{Mult}}} %88.02
+\newcommand{\pmmultax}{\mathop{\text{Mult}} \mathop{\text{ax}}} %88.03
+
+ %Inductive relations
+\newcommand{\pmanc}[1]{#1_\pmast} %90.01
+\newcommand{\pmancc}[1]{\pmcrel{#1}_\pmast} %90.02
+\newcommand{\pmrst}[1]{#1_\text{st}} %91.01
+\newcommand{\pmrts}[1]{#1_\text{ts}} %91.02
+\newcommand{\pmpot}[1]{\text{Pot}\mathbf{`}#1} %91.03
+\newcommand{\pmpotid}[1]{\text{Potid}\mathbf{`}#1} %91.04
+\newcommand{\pmpo}[1]{#1_\text{po}} %91.05
+\newcommand{\pmB}{B} %93.01
+\newcommand{\pmmin}[1]{\text{min}_{#1}} %93.02
+\newcommand{\pmMin}{\text{min}}
+\newcommand{\pmmax}[1]{\text{max}_{#1}} %93.021
+\newcommand{\pmMax}{\text{max}}
+\newcommand{\pmgen}[1]{\text{gen}\mathbf{`}#1} %93.03
+\newcommand{\pmGen}{\text{gen}}
+\newcommand{\pmefr}[2]{#1\pmast#2} %95.05
+\newcommand{\pmipr}[2]{I_{#1}\textbf{`}#2} %96.01
+\newcommand{\pmjpr}[2]{J_{#1}\textbf{`}#2} %96.02
+\newcommand{\pmfr}[2]{\overset{\boldsymbol{\leftrightarrow}}{#1}\textbf{`}#2} %97.01
+
+ %Volume II
+ %Cardinal arithmetic
+ %Definition and Logical Properties of Cardinal Numbers
+\newcommand{\pmnc}[1]{\text{Nc}\textbf{`}#1} %100.01
+\newcommand{\pmNc}{\text{Nc}}
+\newcommand{\pmNC}{\text{NC}} %100.02
+\newcommand{\pmNCat}[2]{\text{NC}^{#1}({#2})} %102.01
+\newcommand{\pmnoc}[1]{\text{N}_0\text{c}\textbf{`}#1} %103.01
+\newcommand{\pmNoc}{\text{N}_0\text{c}}
+\newcommand{\pmNoC}{\text{N}_0\text{C}} %103.02
+\newcommand{\pmnca}[2]{\text{N}^{#1}\text{c}\textbf{`}#2} %104.01, 104.011, etc.
+\newcommand{\pmNca}[1]{\text{N}^{#1}\text{C}} %104.02, 104.021, etc.
+\newcommand{\pmch}[2]{#1^{(#2)}} %104.03, 104.031, etc.
+\newcommand{\pmncd}[2]{\text{N}_{#1}\text{c}\textbf{`}#2} %105.01
+\newcommand{\pmNcd}[1]{\text{N}_{#1}\text{C}} %105.02, 105.021, etc.
+\newcommand{\pmcl}[2]{#1_{(#2)}} %105.03, 105.031, etc.
+\newcommand{\pmncll}[3]{\text{N}_{#1#2}\text{c}\textbf{`}#3} %106.01, 106.012, etc.
+\newcommand{\pmnchh}[3]{\text{N}^{#1#2}\text{c}\textbf{`}#3} %106.011
+\newcommand{\pmncaa}[3]{\text{N}_{#1}{}^{#2}\text{c}\textbf{`}#3} %106.02
+\newcommand{\pmncdd}[3]{{}^{#1}\text{N}_{#2}\text{c}\textbf{`}#3} %106.021
+\newcommand{\pmNCll}[2]{\text{N}_{#1#2}\text{C}} %106.03
+\newcommand{\pmNChh}[2]{\text{N}^{#1#2}\text{C}}
+\newcommand{\pmcll}[3]{#1_{(#2#3)}} %106.04
+\newcommand{\pmchh}[3]{#1^{(#2#3)}} %106.041
+\newcommand{\pmncr}[1]{\text{N}_{00}\text{c}\textbf{`}#1} %106.01
+
+ %Addition, Multiplication, Exponentiation
+\newcommand{\pmarsumc}{\mathrel{+}} %110.01
+\newcommand{\pmarsumnc}{\mathrel{{+}_{\text{c}}}} %110.02
+\newcommand{\pmsmsmb}{\mathrel{\overline{\text{sm}}\;\overline{\text{sm}}}} %111.01
+\newcommand{\pmcrp}[2]{\text{Crp}(#1)\textbf{`}#2} %111.02
+\newcommand{\pmsmsm}{\mathrel{\text{sm}\;\text{sm}}} %111.03
+\newcommand{\pmarsumcc}[1]{\Sigma\textbf{`}#1} %112.01
+\newcommand{\pmarsumcnc}[1]{\Sigma\pmNc\textbf{`}#1} %112.02
+\newcommand{\pmarprodc}{\times} %113.02
+\newcommand{\pmarprodnc}{\times_\text{c}} %113.03
+\newcommand{\pmarprodcnc}[1]{\Pi\pmNc\textbf{`}#1} %114.01
+\newcommand{\pmarprodcc}[1]{\text{Prod}\textbf{`}#1} %115.01
+\newcommand{\pmarcls}{\pmClsn{3}\text{arithm}} %115.02
+\newcommand{\pmarexp}[2]{#1 \mathrel{\text{exp}} #2} %116.01
+\newcommand{\pmArexp}{\text{exp}}
+\newcommand{\pmarncexp}[2]{#1^{#2}} %116.02
+\newcommand{\pmarg}{\mathrel{\boldsymbol{>}}} %117.01
+\newcommand{\pmarl}{\mathrel{\boldsymbol{<}}} %117.04
+\newcommand{\pmargeq}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr${\hspace{-.4ex}\raise-.75ex\hbox{\rotatebox[origin=c]{-155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}$}}} %117.05
+\newcommand{\pmarleq}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth${\raise-.75ex\hbox{\rotatebox[origin=c]{155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}\hspace{-.375ex}$}}} %117.06
+
+ %Finite and infinite
+\newcommand{\pmarsubt}[2]{#1 \mathrel{{-}_\text{c}} #2} %119.01
+\newcommand{\pmArsubt}{{-}_\text{c}}
+\newcommand{\pmNCinduct}{\text{NC}\,\text{induct}} %120.01
+\newcommand{\pmncinduct}[1]{\text{N}_#1\text{C}\,\text{induct}} %120.011
+\newcommand{\pmClsinduct}{\text{Cls}\,\text{induct}} %120.02
+\newcommand{\pmclsinduct}[1]{\text{Cls}_{#1}\,\text{induct}} %120.021
+\newcommand{\pmInfinax}{\text{Infin}\,\text{ax}} %120.03
+\newcommand{\pminfinax}[1]{\text{Infin}\,\text{ax}(#1)} %120.04
+\newcommand{\pmspec}[1]{\text{spec}\textbf{`}#1} %120.43
+\newcommand{\pmintoo}[2]{P(#1\mathbin{\boldsymbol{-}}#2)} %121.01
+\newcommand{\pmintoc}[2]{P({#1}\mathbin{\scalebox{1.2}[.7]{$\boldsymbol{\dashv}$}}{#2})} %121.011
+\newcommand{\pmintco}[2]{P({#1}\mathbin{\scalebox{1.2}[.7]{$\boldsymbol{\vdash}$}}{#2})} %121.012
+\newcommand{\pmintcc}[2]{P({#1} \mathbin{\ooalign{$\scalebox{1.2}[.7]{$\boldsymbol{\dashv}$}$\hidewidth\cr$\scalebox{1.2}[.7]{$\boldsymbol{\vdash}$}$}} {#2})} %121.013
+\newcommand{\pmintnc}[1]{P_{#1}} %121.02
+\newcommand{\pmfinid}[1]{\text{finid}\textbf{`}#1} %121.03
+\newcommand{\pmfin}[1]{\text{fin}\textbf{`}#1} %121.031
+\newcommand{\pmintt}[2]{#1_{#2}} %121.04
+\newcommand{\pmprog}{\text{Prog}} %122.01
+\newcommand{\pmaleph}{\boldsymbol{\aleph}} %123.01
+\newcommand{\pmsucc}{\text{N}} %123.02
+\newcommand{\pmclsrefl}{\text{Cls}\;\text{refl}} %124.01
+\newcommand{\pmncrefl}{\text{NC}\;\text{refl}} %124.02
+\newcommand{\pmncmult}{\text{NC}\;\text{mult}} %124.03
+\newcommand{\pmncind}{\text{NC}\;\text{ind}} %126.01
+\newcommand{\pmnocind}[1]{\text{N}_0\text{Cinduct}\textbf{`}#1}
+\newcommand{\pmNocind}{\text{N}_0\text{Cinduct}}
+
+ %Relation-arithmetic
+ %Ordinal similarity and relation-numbers
+\newcommand{\pmrnsm}[2]{{#1}{\raise.4ex\hbox{\textbf{\large;}}}{#2}} %150.01
+\newcommand{\pmrnsmd}[2]{#1 \mathop{\mathbf{\dagger}} #2} %150.02
+\newcommand{\pmrnsmdf}[1]{#1\mathbf{\dagger}}
+\newcommand{\pmopsc}[2]{#1 \mathrel{\ooalign{${\raise-.7ex\hbox{$\pmdot$}}$\hidewidth\cr$\text{\Female}$\hidewidth\cr${\raise-.8ex\hbox{\hspace{.15cm}\textbf{,}}}$}} #2} %150.03
+\newcommand{\pmsmorb}[2]{#1 \mathrel{\overline{\text{smor}}} #2} %151.01
+\newcommand{\pmSmorb}{\overline{\text{smor}}} %151.01
+\newcommand{\pmsmor}[2]{#1 \mathrel{\text{smor}} #2} %151.02
+\newcommand{\pmSmor}{\text{smor}}
+\newcommand{\pmnr}[1]{\text{Nr}\textbf{`}#1} %152.01
+\newcommand{\pmNr}{\text{Nr}}
+\newcommand{\pmNR}{\text{NR}} %152.02
+\newcommand{\pmsrrn}[1]{{#1}_{s}} %153.01
+\newcommand{\pmNRat}[2]{\text{NR}^{#1}({#2})} %154.01
+\newcommand{\pmnor}[1]{\text{N}_0\text{r}\textbf{`}#1} %155.01
+\newcommand{\pmNor}{\text{N}_0\text{r}}
+\newcommand{\pmNoR}{\text{N}_0\text{R}} %155.02
+
+ %Addition of Relations, and the Product of Two Relations
+\newcommand{\pmrsum}[2]{#1\mathrel{\ooalign{${\raise-.21ex\hbox{$\boldsymbol{-}$}}$\cr\hidewidth$\boldsymbol{\uparrow}$\hidewidth\cr${\raise-.19ex\hbox{$\boldsymbol{-}$}}$}} #2} %160.01
+\newcommand{\pmRsum}{\mathrel{\ooalign{${\raise-.21ex\hbox{$\boldsymbol{-}$}}$\cr\hidewidth$\boldsymbol{\uparrow}$\hidewidth\cr${\raise-.19ex\hbox{$\boldsymbol{-}$}}$}}}
+\newcommand{\pmrsume}[2]{#1 \mathrel{\rotatebox[origin=c]{90}{$\pmRsum$}} #2} %161.01
+\newcommand{\pmRsume}{\rotatebox[origin=c]{90}{$\pmRsum$} }
+\newcommand{\pmrsumb}[2]{#1 \mathrel{\rotatebox[origin=c]{270}{$\pmRsum$}} #2} %161.02
+\newcommand{\pmRsumb}{\rotatebox[origin=c]{270}{$\pmRsum$}}
+\newcommand{\pmrsumr}[1]{\Sigma\textbf{`}#1} %162.01
+\newcommand{\pmRsumr}{\Sigma}
+\newcommand{\pmrsumrex}[1]{\mathrel{\text{Rel}^{#1}\text{excl}}} %163.01
+\newcommand{\pmsmorsmorb}[2]{#1 \mathrel{\overline{\text{smor}}\,\overline{\text{smor}}} #2} %164.01
+\newcommand{\pmSmorsmorb}{\overline{\text{smor}}\,\overline{\text{smor}}}
+\newcommand{\pmsmorsmor}[2]{#1 \mathrel{\pmSmor\,\pmSmor} #2} %164.02
+\newcommand{\pmSmorsmor}{\pmSmor\,\pmSmor}
+\newcommand{\pmrprod}[2]{#1 \times #2} %166.01
+
+ %First differences and the multiplication and exponentiation of relations
+ %On the relation of first differences among the sub-classes of a given class
+\newcommand{\pmrfdcl}[3]{#2 \mathrel{#1_{\text{cl}}} #3} %170.01
+\newcommand{\pmRfdcl}[1]{#1_{\text{cl}}}
+\newcommand{\pmrfdlc}[3]{#2 \mathrel{#1_{\text{lc}}} #3} %170.02
+\newcommand{\pmRfdlc}[1]{#1_{\text{lc}}}
+\newcommand{\pmrfddf}[3]{#2 \mathrel{#1_{\text{df}}} #3} %171.01
+\newcommand{\pmRfddf}[1]{#1_{\text{df}}}
+\newcommand{\pmrfdfd}[3]{#2 \mathrel{#1_{\text{fd}}} #3} %171.02
+\newcommand{\pmRfdfd}[1]{#1_{\text{fd}}}
+\newcommand{\pmrfprod}[1]{\Pi\textbf{`}#1} %172.01
+\newcommand{\pmRfprod}[1]{\text{Prod}\textbf{`}#1} %173.01
+\newcommand{\pmrarrel}[1]{\mathrel{\text{Rel}^{#1}\text{arithm}}} %174.01
+\newcommand{\pmrexp}{\mathrel{\text{exp}}} %176.01
+\newcommand{\pmRexp}[2]{{#1}^{#2}} %176.02
+\newcommand{\pmrnsum}[2]{{#1} + {#2}} %180.01
+\newcommand{\pmRnsum}{+}
+\newcommand{\pmrndsum}[2]{{#1} \mathrel{\pmcirc{+}} {#2}} %180.02
+\newcommand{\pmRndsum}{\pmcirc{+}}
+\newcommand{\pmrnsumru}[2]{#1 \mathrel{\pmcirc{\pmRsumb}} #2} %181.01
+\newcommand{\pmRnsumru}{\pmcirc{\pmRsumb}}
+\newcommand{\pmrnsumur}[2]{#1 \mathrel{\pmcirc{\pmRsume}} #2} %181.011
+\newcommand{\pmRnsumur}{\pmcirc{\pmRsume}}
+\newcommand{\pmrn}[1]{\pmcirc{#1}} %181.02
+\newcommand{\pmrsep}[1]{\ooalign{${\raise1.5ex\hbox{\rotatebox[origin=c]{180}{\scalebox{1.4}[1.4]{$\pmbreve{\phantom{.}}$}}}}$\cr\hidewidth$#1$\hidewidth}} %182.01
+\newcommand{\pmrnsumf}[1]{\Sigma\pmNr\textbf{`}#1} %183.01
+\newcommand{\pmrnprod}[2]{#1 \mathrel{\pmcirc{\times}} #2} %184.01
+\newcommand{\pmRnprod}{\pmcirc{\times}}
+\newcommand{\pmrnprodf}[1]{\Pi\pmNr\textbf{`}#1} %185.01
+\newcommand{\pmrnexp}[3]{#2 \mathrel{\pmArexp_{#1}} #3} %186.01
+\newcommand{\pmRnexp}[1]{\pmArexp_{#1}}
+
+%Series
+%General theory of series
+\newcommand{\pmtrans}{\text{trans}} %201.01
+\newcommand{\pmconnex}{\text{connex}} %202.01
+\newcommand{\pmser}{\text{Ser}} %204.01
+\newcommand{\pmseq}[3]{#1 \mathrel{\text{seq}_{#1}} #2} %206.01
+\newcommand{\pmSeq}[1]{\text{seq}_{#1}}
+\newcommand{\pmprec}[3]{#1 \mathrel{\text{prec}_{#1}} #2} %206.02
+\newcommand{\pmPrec}[1]{\text{prec}_{#1}}
+\newcommand{\pmlt}[1]{\text{lt}_{#1}} %207.01
+\newcommand{\pmtl}[1]{\text{tl}_{#1}} %207.01
+\newcommand{\pmlimax}[2]{\text{limax}_{#1}\textbf{`}#2} %207.03
+\newcommand{\pmLimax}[1]{\text{limax}_{#1}}
+\newcommand{\pmlimin}[2]{\text{limin}_{#1}\textbf{`}#2} %207.04
+\newcommand{\pmLimin}[1]{\text{limin}_{#1}}
+\newcommand{\pmcr}[1]{\text{cr}\textbf{`}{#1}}
+\newcommand{\pmCr}{\text{cr}}
+\newcommand{\pmcror}[1]{\text{cror}\textbf{`}{#1}} %208.01
+\newcommand{\pmCror}{\text{cror}}
+
+%On sections, segments, stretches, and derivatives
+\newcommand{\pmsect}[1]{\text{sect}\textbf{`}{#1}} %211.01
+\newcommand{\pmSect}{\text{sect}}
+\newcommand{\pmseg}[1]{\mathbf{\varsigma}\textbf{`}{#1}} %212.01
+\newcommand{\pmSeg}{\mathbf{\varsigma}}
+\newcommand{\pmsym}[1]{\text{sym}\textbf{`}{#1}} %212.02
+\newcommand{\pmSym}{\text{sym}}
+\newcommand{\pmsectr}[1]{{#1}_{\pmSeg}} %213.01
+\newcommand{\pmded}{\mathrel{\text{Ded}}} %214.01
+\newcommand{\pmsded}{\mathrel{\text{semi}\;\text{Ded}}} %214.02
+\newcommand{\pmstr}[1]{\text{str}\textbf{`}{#1}} %215.01
+\newcommand{\pmStr}{\text{str}}
+\newcommand{\pmder}[2]{\delta_{#1}\textbf{`}#2} %216.01
+\newcommand{\pmDer}[1]{\delta_{#1}}
+\newcommand{\pmdern}[3]{\delta_{#1}^{#2}\textbf{`}#3}
+\newcommand{\pmden}[1]{\text{dense}\textbf{`}{#1}} %216.02
+\newcommand{\pmDen}{\text{dense}}
+\newcommand{\pmclsd}[1]{\text{closed}\textbf{`}{#1}} %216.03
+\newcommand{\pmClsd}{\text{closed}}
+\newcommand{\pmperf}[1]{\text{perf}\textbf{`}{#1}} %216.04
+\newcommand{\pmPerf}{\text{perf}}
+\newcommand{\pmders}[1]{\rotatebox[origin=c]{180}{$\Delta$}\textbf{`}#1} %216.05
+\newcommand{\pmDers}{\rotatebox[origin=c]{180}{$\Delta$}}
+
+%On convergence, and the limits of functions
+\newcommand{\pmconv}[3]{#1\bar{#2}_{\text{cn}}#3} %230.01
+\newcommand{\pmConv}[1]{{#1}_{\text{cn}}} %230.02
+\newcommand{\pmconvg}[3]{#1\bar{#2}_{\text{cng}}#3}
+\newcommand{\pmConvg}[1]{{#1}_{\text{cng}}}
+\newcommand{\pmlsc}[3]{#1\bar{#2}_{\text{sc}}#3} %231.01
+\newcommand{\pmosc}[3]{#1\bar{#2}_{\text{os}}#3} %231.02
+\newcommand{\pmlscl}[4]{(#1\bar{#2}#3)_{\text{sc}}\textbf{`}#4} %232.01
+\newcommand{\pmoscl}[4]{(#1\bar{#2}#3)_{\text{os}}\textbf{`}#4} %232.02
+\newcommand{\pmlmx}[4]{(#1\bar{#2}#3)_{\text{lmx}}\textbf{`}#4} %233.01
+\newcommand{\pmLmx}[3]{(#1\bar{#2}#3)_{\text{lmx}}}
+\newcommand{\pmlimf}[4]{#1(#2#3)\textbf{`}#4} %233.02
+\newcommand{\pmLimf}[3]{#1(#2#3)}
+\newcommand{\pmscf}[3]{\text{sc}(#1, #2)\mathbf{`}#3} %234.01
+\newcommand{\pmosf}[3]{\text{os}(#1, #2)\mathbf{`}#3} %234.02
+\newcommand{\pmctf}[3]{\text{ct}(#1#2)\mathbf{`}#3} %234.03
+\newcommand{\pmcontinf}[3]{\text{contin}(#1#2)\mathbf{`}#3} %234.04
+\newcommand{\pmcontin}[2]{#1 \mathrel{\text{contin}} #2} %234.05
+\newcommand{\pmContin}{\text{contin}}
+
+%Volume III
+%Well-Ordered Series
+\newcommand{\pmbord}{\text{Bord}} %250.01
+\newcommand{\pmword}{\Omega} %250.02
+\newcommand{\pmordn}{\text{NO}} %251.01
+\newcommand{\pmless}{\mathrel{\text{less}}} %254.01
+\newcommand{\pmLess}{\text{less}}
+\newcommand{\pmpsc}[2]{#1 \mathrel{P_{\text{sm}}} #2} %254.02
+\newcommand{\pmPsc}{P_{\text{sm}}}
+\newcommand{\pmorle}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth$\boldsymbol{\cdot}$}}} %255.01
+\newcommand{\pmorgr}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr$\boldsymbol{\cdot}$\hidewidth}}} %255.02
+\newcommand{\pmnoo}{\text{N}_0\text{O}} %255.03
+\newcommand{\pmorleq}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth$\boldsymbol{\cdot}$\cr\hidewidth${\raise-.75ex\hbox{\rotatebox[origin=c]{155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}\hspace{-.375ex}$}}} %255.04
+\newcommand{\pmorgrq}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr$\boldsymbol{\cdot}$\hidewidth\cr${\hspace{-.4ex}\raise-.75ex\hbox{\rotatebox[origin=c]{-155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}$\hidewidth}}} %255.05
+\newcommand{\pmm}{\emph{M}} %256.01
+\newcommand{\pmn}{\emph{N}} %256.02, 263.02
+\newcommand{\pmtranc}[3]{(#1\pmast#2)\textbf{`}#3} %257.01
+\newcommand{\pmTranc}[2]{(#1\pmast#2)} %257.01
+\newcommand{\pmtrpot}[3]{#1_{#2#3}} %257.02
+\newcommand{\pma}{\emph{A}} %259.01
+\newcommand{\pmaw}{\emph{A}_{\emph{W}}} %259.02
+\newcommand{\pmwa}{\emph{W}_{\emph{A}}} %259.03
+
+%Finite and Infinite Series and Ordinals
+\newcommand{\pmintf}{P_{\text{fn}}} %260.01
+\newcommand{\pmserinf}{\text{Ser infin}} %261.01
+\newcommand{\pmwordinf}{\pmword\text{ infin}} %261.02
+\newcommand{\pmserfin}{\text{Ser fin}} %261.03
+\newcommand{\pmwordfin}{\pmword\text{ fin}} %261.04
+\newcommand{\pmwordind}{\pmword\text{ induct}} %261.04
+\newcommand{\pmordnfin}{\text{NO fin}} %262.01
+\newcommand{\pmordninf}{\text{NO infin}} %262.02
+\newcommand{\pmfinord}[1]{#1_r} %262.03
+\newcommand{\pmom}{\boldsymbol{\omega}} %263.01
+\newcommand{\pmpr}[1]{#1_{\text{pr}}} %264.01
+\newcommand{\pmomn}[1]{\pmom_{#1}} %265.01, 265.03, etc.
+\newcommand{\pmalephn}[1]{\pmaleph_{#1}} %265.02, 265.04, etc.
+
+%Compact series, rational series, and continuous series
+\newcommand{\pmcomp}{\mathrel{\text{comp}}} %270.01
+\newcommand{\pmComp}{\text{Comp}}
+\newcommand{\pmmed}{\mathrel{\text{med}}} %271.01
+\newcommand{\pmMed}{\text{med}}
+\newcommand{\pmsimp}[3]{\mathrel{#1_{#2#3}}} %272.01
+\newcommand{\pmsimps}[3]{{#1}_{#2}\textbf{`}{#3}} %273.02
+\newcommand{\pmSimp}[3]{({#1}{#2})_{#3}} %273.03
+\newcommand{\pmSimps}[2]{{#1}_{#2}} %273.04
+\newcommand{\pmrats}{\eta} %273.01
+\newcommand{\pmsfcls}[1]{#1_\pmrats} %274.01
+\newcommand{\pmsfclsm}[2]{#1_m\textbf{`}#2} %274.02
+\newcommand{\pmsfclsp}[2]{\pmbreve{#1}_P\textbf{`}{#2}} %274.03
+\newcommand{\pmsfclsmp}[1]{M_P\textbf{`}{#1}} %274.04
+\newcommand{\pmcser}{\theta} %275.01
+\newcommand{\pmcsercl}[1]{#1_\pmcser} %276.01
+\newcommand{\pmcsercls}[2]{{#1}_{#2}} %276.04
+\newcommand{\pmCsercls}[2]{{#1}_{\text{tl}}\textbf{`}{#2}} %264.05
+%Skipped some temprary definitions as repetitious
+
+%Quantity
+%Generalization of Number
+\newcommand{\pmu}{\textit{U}} %300.01
+\newcommand{\pmrnum}{\text{Rel num}} %300.02
+\newcommand{\pmrnumid}{\text{Rel num id}} %300.03
+\newcommand{\pmrpwr}[2]{#1^#2} %301.03
+\newcommand{\pmPrm}{\text{Prm}} %302.01
+\newcommand{\pmrprm}[4]{(#1,#2)\mathbin{\pmPrm_\tau}(#3,#4)} %302.02
+\newcommand{\pmprm}[4]{(#1,#2)\mathbin{\pmPrm}(#3,#4)} %302.03
+\newcommand{\pmhcf}[2]{\text{hcf}(#1,#2)} %302.04
+\newcommand{\pmHcf}{\text{hcf}}
+\newcommand{\pmlcm}[2]{\text{lcm}(#1,#2)} %302.05
+\newcommand{\pmLcm}{\text{lcm}}
+\newcommand{\pmrat}[2]{#1 \rotatebox[origin=c]{10}{$\boldsymbol{/}$} #2} %303.01
+\newcommand{\pmqn}[1]{#1_q} %303.02
+\newcommand{\pmqnil}{\infty_q} %303.03
+\newcommand{\pmRat}{\text{Rat}} %303.04
+\newcommand{\pmRatdef}{\text{Rat def}} %303.05
+\newcommand{\pmqnle}[2]{#1 \mathrel{\boldsymbol{<}_r} #2} %304.01
+\newcommand{\pmQnle}{\boldsymbol{<}_r}
+\newcommand{\pmqnLe}{H} %304.02
+\newcommand{\pmqnlez}{H'} %304.03
+\newcommand{\pmprodsr}[2]{#1 \times_s #2} %305.01
+\newcommand{\pmProdsr}{\times_s}
+\newcommand{\pmsumsr}[2]{#1 +_s #2} %306.01
+\newcommand{\pmSumsr}{+_s}
+\newcommand{\pmratn}{\text{Rat}_n} %307.01
+\newcommand{\pmratg}{\text{Rat}_g} %307.011
+\newcommand{\pmratnle}[2]{#1 \mathrel{\boldsymbol{<}_n} #2} %307.02
+\newcommand{\pmRatnle}{\boldsymbol{<}_n}
+\newcommand{\pmatngr}[2]{#1 \mathrel{\boldsymbol{>}_n} #2} %307.021
+\newcommand{\pmRatngr}{\boldsymbol{>}_n}
+\newcommand{\pmratgle}[2]{#1 \mathrel{\boldsymbol{<}_g} #2} %307.03
+\newcommand{\pmRatgle}{\boldsymbol{<}_g}
+\newcommand{\pmratggr}[2]{#1 \mathrel{\boldsymbol{>}_g} #2} %307.031
+\newcommand{\pmRatggr}{\boldsymbol{>}_g}
+\newcommand{\pmratnLe}{H_n} %307.04
+\newcommand{\pmratgLe}{H_g} %307.05
+\newcommand{\pmratssub}[2]{#1 \boldsymbol{-}_s #2} %308.01
+\newcommand{\pmsumgr}[2]{#1 +_g #2} %308.02
+\newcommand{\pmprodgr}[2]{#1 \times_g #2} %309.01
+\newcommand{\pmrenp}{\Theta} %310.01
+\newcommand{\pmrenpz}{\Theta'} %310.011
+\newcommand{\pmrenn}{\Theta_n} %310.02
+\newcommand{\pmrennz}{\Theta_n'} %310.021
+\newcommand{\pmreng}{\Theta_g} %310.03
+\newcommand{\pmconc}[1]{\text{concord}(#1)} %311.01
+\newcommand{\pmConc}{\text{concord}}
+\newcommand{\pmrensumc}[2]{#1 +_p #2} %311.02
+\newcommand{\pmrensub}[2]{#1 -_p #2} %312.01
+\newcommand{\pmrensuma}[2]{#1 +_a #2} %312.02
+\newcommand{\pmrenproda}[2]{#1 \times_a #2} %313.01
+\newcommand{\pmrenrsum}[2]{#1 +_r #2} %314.01
+\newcommand{\pmrenrprod}[2]{#1 \times_r #2} %314.02
+\newcommand{\Male}{{\usefont{U}{mvs}{m}{n}\symbol{124}}} %from the Marvosym package
+\newcommand{\pmrenr}{\mathop{\text{\Male}}} %314.03
+\newcommand{\pmrenrssum}[2]{#1 +_\sigma #2} %314.04
+\newcommand{\pmrenrsprod}[2]{#1 \times_\sigma #2} %313.05
+
+%Vector Families
+\newcommand{\pmcorr}[1]{\text{cr}\textbf{`}#1} %330.01
+\newcommand{\pmabel}{\text{Abel}} %330.02
+\newcommand{\pmvfm}[1]{\text{fm}\textbf{`}#1} %330.03
+\newcommand{\pmVfm}{\text{fm}}
+\newcommand{\pmvfmcl}{\textit{FM}} %330.04
+\newcommand{\pmvffb}[1]{#1_\iota} %330.05
+\newcommand{\pmconx}[1]{\text{conx}\textbf{`}#1} %331.01
+\newcommand{\pmconxfm}{\textit{FM}\text{ conx}} %331.02
+\newcommand{\pmfrep}[2]{\text{rep}_#1\textbf{`}#2} %332.01
+\newcommand{\pmfopen}[1]{#1_\partial} %333.01
+\newcommand{\pmfopennid}[1]{#1_{\iota\partial}} %333.011
+\newcommand{\pmfmap}{\textit{FM}\text{ ap}} %333.02
+\newcommand{\pmfmapconx}{\textit{FM}\text{ ap conx}} %333.03
+\newcommand{\pmtrsp}[1]{\text{trs}\textbf{`}#1} %334.01
+\newcommand{\pmfmtrs}{\textit{FM}\text{ trs}} %334.02
+\newcommand{\pmfmconnex}{\textit{FM}\text{ connex}} %334.03
+\newcommand{\pmfmsr}{\textit{FM}\text{ sr}} %334.02
+\newcommand{\pmfmasym}{\textit{FM}\text{ asym}} %334.05
+\newcommand{\pminit}[1]{\text{init}\textbf{`}#1} %335.01
+\newcommand{\pmfminit}{\textit{FM}\text{ init}} %335.02
+\newcommand{\pmvr}[1]{\textit{V}_#1} %336.01
+\newcommand{\pmvrnid}[1]{\textit{U}_#1} %336.011
+\newcommand{\pmarvs}[1]{A_{#1}} %336.02
+
+%Measurement
+\newcommand{\pmfmsubm}{\textit{FM}\text{ subm}} %351.01
+\newcommand{\pmvrm}[2]{#1_#2} %352.01
+\newcommand{\pmvrmg}[2]{#1_{#2\iota}} %352.02
+\newcommand{\pmfmrt}{\textit{FM}\text{ rt}} %353.01
+\newcommand{\pmfmcx}{\textit{FM}\text{ cx}} %353.02
+\newcommand{\pmfmrtcx}{\textit{FM}\text{ rt cx}} %353.03
+\newcommand{\pmfmg}[1]{#1_g} %354.01
+\newcommand{\pmrtnet}[2]{\text{cx}_#1\textbf{`}#2} %354.02
+\newcommand{\pmfmgrp}{\textit{FM}\text{ grp}} %354.03
+\newcommand{\pmrems}[2]{#1_#2} %356.01
+
+%Cyclic Families
+\newcommand{\pmfmcycl}{\textit{FM}\text{ cycl}} %370.01
+\newcommand{\pmcycl}[2]{#1_#2} %370.02
+\newcommand{\pmcycli}[2]{#1_#2} %370.03
+\newcommand{\pmvser}[2]{#1_#2} %371.01
+\newcommand{\pmintsecvser}[2]{#1_#2} %372.01
+\newcommand{\pmprime}{\text{Prime}} %373.01
+\newcommand{\pmsfmid}[3]{#1_{#2#3}} %373.02
+\newcommand{\pmsmltid}[2]{(#1, #2)} %373.03
+\newcommand{\pmprrt}[3]{(#1 \rotatebox[origin=c]{10}{$\boldsymbol{/}$} #2)_{#3}} %375.01
+
+\begin{document}
+
+\chapter*{\centering LIST OF DEFINITIONS}
+\onehalfspacing
+\begin{tabular}{l l}
+ \text{ }$\pmast1\pmcdot01$. & $p \pmimp q$ \\
+ \text{ }$\pmast2\pmcdot33$. & $p \pmor q \pmor r$ \\
+ \text{ }$\pmast3\pmcdot01$. & $p \pmand q$ \\
+ \text{ }$\pmast3\pmcdot02$. & $p \pmimp q \pmimp r$ \\
+ \text{ }$\pmast4\pmcdot01$. & $p \pmiff q$ \\
+ \text{ }$\pmast4\pmcdot02$. & $p \pmiff q \pmiff r$ \\
+ \text{ }$\pmast4\pmcdot34$. & $p \pmand q \pmand r$ \\
+ \text{ }$\pmast9\pmcdot01$. & $\pmnot\{\pmall{x}\pmdot \phi x\}$ \\
+ \text{ }$\pmast9\pmcdot011$. & $\pmnot\pmall{x}\pmdot \phi x$ \\
+ \text{ }$\pmast9\pmcdot02$. & $\pmnot\{\pmsome{x}\pmdot \phi x\}$ \\
+ \text{ }$\pmast9\pmcdot021$. & $\pmnot\pmsome{x}\pmdot \phi x$ \\
+ \text{ }$\pmast9\pmcdot03$. & $\pmall{x}\pmdot \phi x \pmdot \pmor \pmdot p$ \\
+ \text{ }$\pmast9\pmcdot04$. & $p \pmdot \pmor \pmdot \pmall{x}\pmdot \phi x$ \\
+ \text{ }$\pmast9\pmcdot05$. & $\pmsome{x}\pmdot \phi x \pmdot \pmor \pmdot p$ \\
+ \text{ }$\pmast9\pmcdot06$. & $p \pmdot \pmor \pmdot \pmsome{x}\pmdot \phi x$ \\
+ \text{ }$\pmast9\pmcdot07$. & $\pmall{x}\pmdot \phi x \pmdot \pmor \pmdot \pmsome{y}\pmdot \psi y$ \\
+ \text{ }$\pmast9\pmcdot08$. & $\pmsome{y}\pmdot \psi y \pmdot \pmor \pmdot \pmall{x}\pmdot \phi x$ \\
+ $\pmast10\pmcdot01$. & $\pmsome{x}\pmdot \phi x$ \\
+ $\pmast10\pmcdot02$. & $\phi x \pmimp_x \psi x$ \\
+ $\pmast10\pmcdot03$. & $\phi x \pmiff_x \psi x$ \\
+ $\pmast11\pmcdot01$. & $\pmall{x,y}\pmdot \phi(x, y)$ \\
+ $\pmast11\pmcdot02$. & $\pmall{x,y,z}\pmdot \phi(x, y, z)$ \\
+ $\pmast11\pmcdot03$. & $\pmsome{x,y}\pmdot \phi(x, y)$ \\
+ $\pmast11\pmcdot04$. & $\pmsome{x,y,z}\pmdot \phi(x, y, z)$ \\
+ $\pmast11\pmcdot05$. & $\phi(x, y) \pmdot\pmimp_{x, y}\pmdot \psi(x, y)$ \\
+ $\pmast11\pmcdot06$. & $\phi(x, y) \pmdot\pmiff_{x, y}\pmdot \psi(x, y)$ \\
+ $\pmast13\pmcdot01$. & $x = y$ \\
+ $\pmast13\pmcdot02$. & $x \pmnid y$
+\end{tabular}
+
+\begin{tabular}{l l}
+ $\pmast13\pmcdot03$. & $x = y = z$ \\
+ $\pmast14\pmcdot01$. & $[\pmdsc{x}(\phi x)]\pmdot \psi\pmdsc{x}(\phi x)$ \\
+ $\pmast14\pmcdot02$. & $\pmexists\pmdsc{x}(\phi x)$ \\
+ $\pmast14\pmcdot03$. & $[\pmdsc{x}(\phi x), \pmdsc{x}(\psi x)]\pmdot f\{\pmdsc{x}(\phi x),$\\
+ & \indent $\pmdsc{x}(\psi x)\}$ \\
+ $\pmast14\pmcdot04$. & $[\pmdsc{x}(\psi x)]\pmdot f\{\pmdsc{x}(\phi x), \pmdsc{x}(\psi x)\}$ \\
+ $\pmast20\pmcdot01$. & $f\{\pmcls{z}{\psi z}\}$ \\
+ $\pmast20\pmcdot02$. & $x \mathrel{\pmcin} (\pmpred{\phi}{\pmhat{z}})$ \\
+ $\pmast20\pmcdot03$. & $\pmCls$ \\
+ $\pmast20\pmcdot04$. & $x, y \pmcin \alpha$ \\
+ $\pmast20\pmcdot05$. & $x, y, z \pmcin \alpha$ \\
+ $\pmast20\pmcdot06$. & $x \pmnot \pmcin \alpha$ \\
+ $\pmast20\pmcdot07$. & $\pmall{\alpha}\pmdot f\alpha$ \\
+ $\pmast20\pmcdot071$. & $\pmsome{\alpha}\pmdot f\alpha$ \\
+ $\pmast20\pmcdot072$. & $[\pmdsc{\alpha}(\phi \alpha)]\pmdot f\pmdsc{\alpha}(\phi \alpha)$ \\
+ $\pmast20\pmcdot08$. & $f\{\pmcls{\alpha}{\psi \alpha}\}$ \\
+ $\pmast20\pmcdot081$. & $\alpha \pmcin \pmpred{\psi}{\alpha}$ \\
+ $\pmast21\pmcdot01$. & $f\{\pmrel{x}{y}{\psi(x,y)}\}$ \\
+ $\pmast21\pmcdot02$. & $\pmrelep{a}{\pmpredd{\phi}{\pmhat{x}}{\pmhat{y}}}{b}$ \\
+ $\pmast21\pmcdot03$. & $\pmRel$ \\
+ $\pmast21\pmcdot07$. & $\pmall{R}\pmdot fR$ \\
+ $\pmast21\pmcdot071$. & $\pmsome{R}\pmdot fR$ \\
+ $\pmast21\pmcdot072$. & $[\pmdsc{R}(\phi R)]\pmdot f\pmdsc{R}(\phi R)$ \\
+ $\pmast21\pmcdot08$. & $f\{\pmrel{R}{S}{\psi(R, S)}\}$ \\
+ $\pmast21\pmcdot081$. & $\pmrelep{P}{\pmpredd{\phi}{\pmhat{R}}{\pmhat{S}}}{Q}$ \\
+ $\pmast21\pmcdot082$. & $f\{\pmcls{R}{\psi R}\}$ \\
+ $\pmast21\pmcdot083$. & $R \pmcin \pmpred{\phi}{\pmhat{R}}$ \\
+ $\pmast22\pmcdot01$. & $\alpha \pmcinc \beta$ \\
+ $\pmast22\pmcdot02$. & $\alpha \pmccap \beta$
+\end{tabular}
+
+\begin{tabular}{l l}
+$\pmast22\pmcdot03$. & $\alpha \pmccup \beta$ \\
+$\pmast22\pmcdot04$. & $\pmccmp{\alpha}$ \\
+$\pmast22\pmcdot05$. & $\pmcmin{\alpha}{\beta}$ \\
+$\pmast22\pmcdot53$. & $\alpha \pmccap \beta \pmccap \gamma$ \\
+$\pmast22\pmcdot71$. & $\alpha \pmccup \beta \pmccup \gamma$ \\
+$\pmast23\pmcdot01$. & $R \pmrinc S$ \\
+$\pmast23\pmcdot02$. & $R \pmrcap S$ \\
+$\pmast23\pmcdot03$. & $R \pmrcup S$ \\
+$\pmast23\pmcdot04$. & $\pmrcmp{R}$ \\
+$\pmast23\pmcdot05$. & $\pmrmin{R}{S}$ \\
+$\pmast23\pmcdot53$. & $R \pmrcap S \pmrcap T$ \\
+$\pmast23\pmcdot71$. & $R \pmrcup S \pmrcup T$ \\
+$\pmast24\pmcdot01$. & $\pmcuni$ \\
+$\pmast24\pmcdot02$. & $\pmcnull$ \\
+$\pmast24\pmcdot03$. & $\pmcexists \alpha$ \\
+$\pmast25\pmcdot01$. & $\pmruni$ \\
+$\pmast25\pmcdot02$. & $\pmrnull$ \\
+$\pmast25\pmcdot03$. & $\pmrexists R$ \\
+$\pmast30\pmcdot01$. & $\pmdscf{R}{y}$ \\
+$\pmast30\pmcdot02$. & $\pmdscf{R}{\pmdscf{S}{y}}$ \\
+$\pmast31\pmcdot01$. & $\pmCnv$ \\
+$\pmast31\pmcdot02$. & $\pmcrel{P}$ \\
+$\pmast32\pmcdot01$. & $\pmRrf{R}$ \\
+$\pmast32\pmcdot02$. & $\pmRrl{R}$ \\
+$\pmast32\pmcdot03$. & $\pmSg$ \\
+$\pmast32\pmcdot04$. & $\pmGs$ \\
+$\pmast33\pmcdot01$. & $\pmDm$ \\
+$\pmast33\pmcdot02$. & $\pmCdm$ \\
+$\pmast33\pmcdot03$. & $\pmCmp$ \\
+$\pmast33\pmcdot04$. & $\pmFld$ \\
+$\pmast34\pmcdot01$. & $\pmrprd{R}{S}$ \\
+$\pmast34\pmcdot02$. & $\pmrprdn{R}{2}$
+\end{tabular}
+
+\begin{tabular}{l l}
+$\pmast34\pmcdot03$. & $\pmrprdn{R}{3}$ \\
+$\pmast35\pmcdot01$. & $\pmrld{\alpha}{R}$ \\
+$\pmast35\pmcdot02$. & $\pmrlcd{R}{\beta}$ \\
+$\pmast35\pmcdot03$. & $\pmrlf{\alpha}{R}{\beta}$ \\
+$\pmast35\pmcdot04$. & $\pmrl{\alpha}{\beta}$ \\
+$\pmast35\pmcdot05$. & $\pmrl{\pmdscf{R}{x}}{\beta}$ \\
+$\pmast35\pmcdot24$. & $\pmrld{\alpha}{\pmrprd{R}{S}}$ \\
+$\pmast35\pmcdot25$. & $\pmrlcd{\pmrprd{S}{R}}{\alpha}$ \\
+$\pmast36\pmcdot01$. & $\pmrlF{P}{\alpha}$ \\
+$\pmast37\pmcdot01$. & $\pmdscff{R}{\beta}$ \\
+$\pmast37\pmcdot02$. & $\pmdscfR{R}$ \\
+$\pmast37\pmcdot03$. & ${\pmdscfR{\pmcrel{R}}}$\\
+$\pmast37\pmcdot04$. & $\pmdscfff{R}{\kappa}$ \\
+$\pmast37\pmcdot05$. & $\pmdscfe{R}{\beta}$ \\
+$\pmast38\pmcdot01$. & $x \pmop$ \\
+$\pmast38\pmcdot02$. & $\pmop y$ \\
+$\pmast38\pmcdot03$. & $\pmopc{\alpha}{y}$\\
+$\pmast40\pmcdot01$. & $\pmccsum{\kappa}$ \\
+$\pmast40\pmcdot02$. & $\pmccprd{\kappa}$ \\
+$\pmast41\pmcdot01$. & $\pmcrsum{\lambda}$ \\
+$\pmast41\pmcdot02$. & $\pmcrprd{\lambda}$ \\
+$\pmast43\pmcdot01$. & $\pmrprdd{R}{S}$ \\
+$\pmast50\pmcdot01$. & $\pmrid$ \\
+$\pmast50\pmcdot02$. & $\pmrdiv$ \\
+$\pmast51\pmcdot01$. & $\pmcUnit$ \\
+$\pmast52\pmcdot01$. & $\pmcn{1}$ \\
+$\pmast54\pmcdot01$. & $\pmcn{0}$ \\
+$\pmast54\pmcdot02$. & $\pmcn{2}$ \\
+$\pmast55\pmcdot01$. & $\pmoc{x}{y}$ \\
+$\pmast55\pmcdot02$. & $\pmoc{\pmdscf{R}{x}}{y}$ \\
+$\pmast56\pmcdot01$. & $\pmdn{2}$ \\
+$\pmast56\pmcdot02$. & $\pmorn{2}$
+\end{tabular}
+
+\begin{tabular}{l l}
+$\pmast56\pmcdot03$. & $\pmorn{0}$ \\
+$\pmast60\pmcdot01$. & $\pmsCl$ \\
+$\pmast60\pmcdot02$. & $\pmsCle$ \\
+$\pmast60\pmcdot03$. & $\pmClsn{2}$ \\
+$\pmast60\pmcdot04$. & $\pmClsn{3}$ \\
+$\pmast61\pmcdot01$. & $\pmsRl$ \\
+$\pmast61\pmcdot02$. & $\pmsRle$ \\
+$\pmast61\pmcdot03$. & $\pmReln{2}$ \\
+$\pmast61\pmcdot04$. & $\pmReln{3}$ \\
+$\pmast62\pmcdot01$. & $\pmrin$ \\
+$\pmast63\pmcdot01$. & $\pmrt{x}$ \\
+$\pmast63\pmcdot011$. & $\pmrti{1}{x}$ \\
+$\pmast63\pmcdot02$. & $\pmrtc{0}{\alpha}$ \\
+$\pmast63\pmcdot03$. & $\pmrtc{1}{\kappa}$ \\
+$\pmast63\pmcdot04$. & $\pmrti{2}{\kappa}$ \\
+$\pmast63\pmcdot041$. & $\pmrti{3}{\kappa}$ \\
+$\pmast63\pmcdot05$. & $\pmrtc{2}{\kappa}$ \\
+$\pmast63\pmcdot051$. & $\pmrtc{3}{\kappa}$ \\
+$\pmast64\pmcdot01$. & $\pmrtrc{00}{\alpha}$ \\
+$\pmast64\pmcdot011$. & $\pmrtri{11}{x}$ \\
+$\pmast64\pmcdot012$. & $\pmrti{12}{x}$ \\
+$\pmast64\pmcdot013$. & $\pmrti{21}{x}$ \\
+$\pmast64\pmcdot014$. & $\pmrti{22}{x}$ \\
+$\pmast64\pmcdot02$. & $\pmrtc{01}{\alpha}$ \\
+$\pmast64\pmcdot021$. & $\pmrtc{10}{\alpha}$ \\
+$\pmast64\pmcdot022$. & $\pmrtc{11}{\alpha}$ \\
+$\pmast64\pmcdot03$. & $\pmrtrci{0}{1}{\alpha}$ \\
+$\pmast64\pmcdot031$. & $\pmrtrci{1}{1}{\alpha}$ \\
+$\pmast64\pmcdot04$. & $\pmrtric{1}{0}{\alpha}$ \\
+$\pmast64\pmcdot041$. & $\pmrtric{1}{1}{\alpha}$ \\
+$\pmast65\pmcdot01$. & $\pmrtdi{\alpha}{x}$ \\
+$\pmast65\pmcdot02$. & $\pmrtdc{\alpha}{x}$
+\end{tabular}
+
+\begin{tabular}{l l}
+$\pmast65\pmcdot03$. & $\pmrtdri{R}{x}$ \\
+$\pmast65\pmcdot04$. & $\pmrtdrc{R}{x}$ \\
+$\pmast65\pmcdot1$. & $\pmrtdri{R}{(x,y)}$ \\
+$\pmast65\pmcdot11$. & $\pmrtdrc{R}{x_y}$\\
+$\pmast65\pmcdot12$. & $\pmrtdrc{R}{x, y}$ \\
+$\pmast70\pmcdot01$. & $\pmrdc{\alpha}{\beta}$ \\
+$\pmast73\pmcdot01$. & $\alpha \pmsmbar \beta$ \\
+$\pmast73\pmcdot02$. & $\pmsm$\\
+$\pmast80\pmcdot01$. & $\pmSelp$ \\
+$\pmast84\pmcdot01$. & $\pmexc$ \\
+$\pmast84\pmcdot02$. & $\pmexcc{\gamma}$ \\
+$\pmast84\pmcdot03$. & $\pmexcn$\\
+$\pmast85\pmcdot5$. & $\pmselc{P}{\,y}$ \\
+$\pmast88\pmcdot01$. & $\pmmultr$ \\
+$\pmast88\pmcdot02$. & $\pmmultc$ \\
+$\pmast88\pmcdot03$. & $\pmmultax$ \\
+$\pmast90\pmcdot01$. & $\pmanc{R}$ \\
+$\pmast90\pmcdot02$. & $\pmancc{R}$ \\
+$\pmast91\pmcdot01$. & $\pmrst{R}$ \\
+$\pmast91\pmcdot02$. & $\pmrts{R}$ \\
+$\pmast91\pmcdot03$. & $\pmpot{R}$ \\
+$\pmast91\pmcdot04$. & $\pmpotid{R}$ \\
+$\pmast91\pmcdot05$. & $\pmpo{R}$ \\
+$\pmast93\pmcdot01$. & $\pmB$ \\
+$\pmast93\pmcdot02$. & $\pmmin{P}$ \\
+$\pmast93\pmcdot021$. & $\pmmax{P}$ \\
+$\pmast93\pmcdot03$. & $\pmgen{P}$ \\
+$\pmast95\pmcdot01$. & $\pmefr{P}{Q}$ \hspace{.3cm} Dft [$\pmast95$] \\
+$\pmast96\pmcdot01$. & $\pmipr{R}{x}$ \hspace{.415cm} Dft [$\pmast96$] \\
+$\pmast96\pmcdot02$. & $\pmjpr{R}{x}$ \hspace{.375cm} Dft [$\pmast96$] \\
+$\pmast97\pmcdot01$. & $\pmfr{R}{x}$ \\
+$\pmast100\pmcdot01$. & $\pmNc$
+\end{tabular}
+
+\onehalfspacing
+\begin{tabular}{l l}
+ $\pmast100\pmcdot02$. & $\pmNC$ \\
+ $\pmast102\pmcdot01$. & $\pmNCat{\beta}{\alpha}$ \\
+ $\pmast103\pmcdot01$. & $\pmnoc{\alpha}$ \\
+ $\pmast103\pmcdot02$. & $\pmNoC$ \\
+ $\pmast104\pmcdot01$. & $\pmnca{1}{\alpha}$ \\
+ $\pmast104\pmcdot011$. & $\pmnca{2}{\alpha}$ \\
+ $\pmast104\pmcdot02$. & $\pmNca{1}$ \\
+ $\pmast104\pmcdot021$. & $\pmNca{2}$ \\
+ $\pmast104\pmcdot03$. & $\pmch{\mu}{1}$ \\
+ $\pmast104\pmcdot031$. & $\pmch{\mu}{2}$ \\
+ $\pmast105\pmcdot01$. & $\pmncd{1}{\alpha}$ \\
+ $\pmast105\pmcdot011$. & $\pmncd{2}{\alpha}$ \\
+ $\pmast105\pmcdot02$. & $\pmNcd{1}$ \\
+ $\pmast105\pmcdot021$. & $\pmNcd{2}$ \\
+ $\pmast105\pmcdot03$. & $\pmcl{\mu}{1}$ \\
+ $\pmast105\pmcdot031$. & $\pmcl{\mu}{2}$ \\
+ $\pmast106\pmcdot01$. & $\pmncll{0}{0}{\alpha}$ \\
+ $\pmast106\pmcdot011$. & $\pmnchh{1}{1}{\alpha}$ \\
+ $\pmast106\pmcdot012$. & $\pmncll{0}{1}{\alpha}$ \\
+ $\pmast106\pmcdot02$. & $\pmncaa{0}{1}{\alpha}$ \\
+ $\pmast106\pmcdot021$. & $\pmncdd{1}{0}{\alpha}$ \\
+ $\pmast106\pmcdot03$. & $\pmNCll{0}{0}$ \\
+ $\pmast106\pmcdot04$. & $\pmcll{\mu}{0}{0}$ \\
+ $\pmast106\pmcdot041$. & $\pmchh{\mu}{1}{1}$ \\
+ $\pmast110\pmcdot01$. & $\alpha \pmarsumc \beta$ \\
+ $\pmast110\pmcdot02$. & $\mu \pmarsumnc \nu$ \\
+ $\pmast110\pmcdot03$. & $\pmnc{\alpha} \pmarsumnc \mu$ \\
+ $\pmast110\pmcdot04$. & $\mu \pmarsumnc \pmnc{\alpha}$ \\
+ $\pmast110\pmcdot0561$. & $\mu \pmarsumnc \nu \pmarsumnc \varpi$ \\
+ $\pmast111\pmcdot01$. & $\kappa \pmsmsmb \lambda$ \\
+ $\pmast111\pmcdot02$. & $\pmcrp{S}{\beta}$ \\
+ $\pmast111\pmcdot03$. & $\pmsmsm$
+\end{tabular}
+
+\begin{tabular}{l l}
+ $\pmast112\pmcdot01$. & $\pmarsumcc{\kappa}$ \\
+ $\pmast112\pmcdot02$. & $\pmarsumcnc{\kappa}$ \\
+ $\pmast113\pmcdot02$. & $\beta \pmarprodc \alpha$ \\
+ $\pmast113\pmcdot03$. & $\mu \pmarprodnc \nu$ \\
+ $\pmast113\pmcdot04$. & $\pmnc{\beta} \pmarprodnc \mu$ \\
+ $\pmast113\pmcdot05$. & $\mu \pmarprodnc \pmnc{\alpha}$ \\
+ $\pmast113\pmcdot511$. & $\alpha \pmarprodc \beta \pmarprodc \gamma$ \\
+ $\pmast113\pmcdot541$. & $\mu \pmarprodnc \nu \pmarprodnc \varpi$ \\
+ $\pmast114\pmcdot01$. & $\pmarprodcnc{\kappa}$ \\
+ $\pmast115\pmcdot01$. & $\pmarprodcc{\kappa}$ \\
+ $\pmast115\pmcdot02$. & $\pmarcls$ \\
+ $\pmast116\pmcdot01$. & $\pmarexp{\alpha}{\beta}$ \\
+ $\pmast116\pmcdot02$. & $\pmarncexp{\mu}{\nu}$ \\
+ $\pmast116\pmcdot03$. & $\pmarncexp{(\pmnc{\alpha})}{\nu}$ \\
+ $\pmast116\pmcdot04$. & $\pmarncexp{\mu}{\pmnc{\beta}}$ \\
+ $\pmast117\pmcdot01$. & $\mu \pmarg \nu$ \\
+ $\pmast117\pmcdot02$. & $\mu \pmarg \pmnc{\alpha}$ \\
+ $\pmast117\pmcdot03$. & $\pmnc{\alpha} \pmarg \nu$ \\
+ $\pmast117\pmcdot04$. & $\mu \pmarl \nu$ \\
+ $\pmast117\pmcdot05$. & $\mu \pmargeq \nu$ \\
+ $\pmast117\pmcdot06$. & $\mu \pmarleq \nu$ \\
+ $\pmast119\pmcdot01$. & $\pmarsubt{\gamma}{\nu}$ \\
+ $\pmast119\pmcdot02$. & $\pmarsubt{\pmnc{\alpha}}{\nu}$ \\
+ $\pmast119\pmcdot03$. & $\pmarsubt{\gamma}{\pmnc{\beta}}$ \\
+ $\pmast120\pmcdot01$. & $\pmNCinduct$ \\
+ $\pmast120\pmcdot011$. & $\pmncinduct{\xi}$ \\
+ $\pmast120\pmcdot02$. & $\pmClsinduct$ \\
+ $\pmast120\pmcdot021$. & $\pmclsinduct{\xi}$ \\
+ $\pmast120\pmcdot03$. & $\pmInfinax$ \\
+ $\pmast120\pmcdot04$. & $\pminfinax{x}$ \\
+ $\pmast120\pmcdot43$. & $\pmspec{\beta}$ \\
+ $\pmast121\pmcdot01$. & $\pmintoo{x}{y}$
+\end{tabular}
+
+\begin{tabular}{l l}
+ $\pmast121\pmcdot011$. & $\pmintoc{x}{y}$ \\
+ $\pmast121\pmcdot012$. & $\pmintco{x}{y}$ \\
+ $\pmast121\pmcdot013$. & $\pmintcc{x}{y}$ \\
+ $\pmast121\pmcdot02$. & $\pmintnc{\nu}$ \\
+ $\pmast121\pmcdot03$. & $\pmfinid{P}$ \\
+ $\pmast121\pmcdot031$. & $\pmfin{P}$ \\
+ $\pmast121\pmcdot04$. & $\pmintt{\nu}{P}$ \\
+ $\pmast122\pmcdot01$. & $\pmprog$ \\
+ $\pmast123\pmcdot01$. & $\pmalephn{0}$ \\
+ $\pmast123\pmcdot02$. & $\pmsucc$ Dft [$\pmast123\textbf{---}4$] \\
+ $\pmast124\pmcdot01$. & $\pmclsrefl$ \\
+ $\pmast124\pmcdot02$. & $\pmncrefl$ \\
+ $\pmast124\pmcdot021$. & $\pmnc{\rho}\pmcin \pmncrefl$ \\
+ $\pmast124\pmcdot03$. & $\pmncmult$ \\
+ $\pmast126\pmcdot01$. & $\pmncind$ \\
+ $\pmast150\pmcdot01$. & $\pmrnsm{S}{Q}$ \\
+ $\pmast150\pmcdot02$. & $\pmrnsmd{S}{Q}$ \\
+ $\pmast150\pmcdot03$. & $\pmopsc{Q}{y}$ \\
+ $\pmast150\pmcdot04$. & $\pmdscf{R}{\pmrnsm{S}{Q}}$ \\
+ $\pmast150\pmcdot05$. & $\pmrnsm{R}{\pmrnsm{S}{Q}}$ \\
+ $\pmast151\pmcdot01$. & $\pmsmorb{P}{Q}$ \\
+ $\pmast151\pmcdot02$. & $\pmSmor$ \\
+ $\pmast152\pmcdot01$. & $\pmNr$ \\
+ $\pmast152\pmcdot02$. & $\pmNR$ \\
+ $\pmast153\pmcdot01$. & $\pmsrrn{1}$ \\
+ $\pmast154\pmcdot01$. & $\pmNRat{\gamma}{X}$ \\
+ $\pmast155\pmcdot01$. & $\pmnor{P}$ \\
+ $\pmast155\pmcdot02$. & $\pmNoR$ \\
+ $\pmast160\pmcdot01$. & $\pmrsum{P}{Q}$ \\
+ $\pmast161\pmcdot01$. & $\pmrsumb{P}{x}$ \\
+ $\pmast161\pmcdot02$. & $\pmrsume{x}{P}$ \\
+ $\pmast161\pmcdot212$. & $\pmrsumb{P}{\pmrsumb{x}{y}}$
+\end{tabular}
+
+\begin{tabular}{l l}
+ $\pmast161\pmcdot213$. & $\pmrsume{\pmrsume{x}{y}}{P}$ \\
+ $\pmast162\pmcdot01$. & $\pmrsumr{P}$ \\
+ $\pmast163\pmcdot01$. & $\pmrsumrex{2}$ \\
+ $\pmast164\pmcdot01$. & $\pmsmorsmorb{P}{Q}$ \\
+ $\pmast164\pmcdot02$. & $\pmSmorsmor$ \\
+ $\pmast166\pmcdot01$. & $\pmrprod{Q}{P}$ \\
+ $\pmast166\pmcdot421$. & $\pmrprod{P}{\pmrprod{Q}{R}}$ \\
+ $\pmast170\pmcdot01$. & $\pmRfdcl{P}$ \\
+ $\pmast170\pmcdot02$. & $\pmRfdlc{P}$ \\
+ $\pmast171\pmcdot01$. & $\pmRfddf{P}$ \\
+ $\pmast171\pmcdot02$. & $\pmRfdfd{P}$ \\
+ $\pmast172\pmcdot01$. & $\pmrfprod{P}$ \\
+ $\pmast173\pmcdot01$. & $\pmRfprod{P}$ \\
+ $\pmast174\pmcdot01$. & $\pmrarrel{3}$ \\
+ $\pmast176\pmcdot01$. & $P \pmrexp Q$ \\
+ $\pmast176\pmcdot02$. & $\pmRexp{P}{Q}$ \\
+ $\pmast180\pmcdot01$. & $\pmrnsum{P}{Q}$ \\
+ $\pmast180\pmcdot02$. & $\pmrndsum{\mu}{\nu}$ \\
+ $\pmast180\pmcdot03$. & $\pmrndsum{\pmnr{P}}{\nu}$ \\
+ $\pmast180\pmcdot04$. & $\pmrndsum{\mu}{\pmnr{Q}}$ \\
+ $\pmast180\pmcdot561$. & $\pmrndsum{\mu}{\pmrndsum{\nu}{\varpi}}$ \\
+ $\pmast181\pmcdot01$. & $\pmrnsumru{P}{x}$ \\
+ $\pmast181\pmcdot011$. & $\pmrnsumur{x}{P}$ \\
+ $\pmast181\pmcdot02$. & $\pmrndsum{\mu}{\pmrn{1}}$ \\
+ $\pmast181\pmcdot021$. & $\pmrndsum{\pmrn{1}}{\mu}$ \\
+ $\pmast181\pmcdot03$. & $\pmrndsum{\pmnr{P}}{\pmrn{1}}$ \\
+ $\pmast181\pmcdot031$. & $\pmrndsum{\pmrn{1}}{\pmnr{P}}$ \\
+ $\pmast181\pmcdot04$. & $\pmrndsum{\pmrn{1}}{\pmrn{1}}$ \\
+ $\pmast181\pmcdot561$. & $\pmrndsum{\mu}{\pmrndsum{\pmrn{1}}{\pmrn{1}}}$ \\
+ $\pmast181\pmcdot571$. & $\pmrndsum{\pmrn{1}}{\pmrndsum{\pmrn{1}}{\mu}}$ \\
+ $\pmast182\pmcdot01$. & $\pmrsep{\pmop}$ \\
+ $\pmast183\pmcdot01$. & $\pmrnsumf{P}$
+\end{tabular}
+
+\begin{tabular}{l l}
+ $\pmast184\pmcdot01$. & $\pmrnprod{\mu}{\nu}$ \\
+ $\pmast184\pmcdot02$. & $\pmrnprod{\pmnr{P}}{\nu}$ \\
+ $\pmast184\pmcdot03$. & $\pmrnprod{\mu}{\pmnr{Q}}$ \\
+ $\pmast184\pmcdot32$. & $\pmrnprod{\mu}{\pmrnprod{\nu}{\varpi}}$ \\
+ $\pmast185\pmcdot01$. & $\pmrnprodf{P}$ \\
+ $\pmast186\pmcdot01$. & $\pmrnexp{r}{\mu}{\nu}$ \\
+ $\pmast186\pmcdot02$. & $\pmrnexp{r}{(\pmnr{P})}{\nu}$ \\
+ $\pmast186\pmcdot03$. & $\pmrnexp{r}{\mu}{(\pmnr{Q})}$ \\
+ $\pmast201\pmcdot01$. & $\pmtrans$ \\
+ $\pmast202\pmcdot01$. & $\pmconnex$ \\
+ $\pmast204\pmcdot01$. & $\pmser$ \\
+ $\pmast206\pmcdot01$. & $\pmSeq{P}$ \\
+ $\pmast206\pmcdot02$. & $\pmPrec{P}$ \\
+ $\pmast207\pmcdot01$. & $\pmlt{P}$ \\
+ $\pmast207\pmcdot02$. & $\pmtl{P}$ \\
+ $\pmast207\pmcdot03$. & $\pmLimax{P}$ \\
+ $\pmast207\pmcdot04$. & $\pmLimin{P}$ \\
+ $\pmast208\pmcdot01$. & $\pmcror{P}$ \\
+ $\pmast211\pmcdot01$. & $\pmsect{P}$ \\
+ $\pmast212\pmcdot01$. & $\pmseg{P}$ \\
+ $\pmast212\pmcdot02$. & $\pmsym{P}$ \\
+ $\pmast213\pmcdot01$. & $\pmsectr{P}$ \\
+ $\pmast214\pmcdot01$. & $\pmded$ \\
+ $\pmast214\pmcdot02$. & $\pmsded$ \\
+ $\pmast215\pmcdot01$. & $\pmstr{P}$ \\
+ $\pmast216\pmcdot01$. & $\pmDer{P}$ \\
+ $\pmast216\pmcdot02$. & $\pmden{P}$ \\
+ $\pmast216\pmcdot03$. & $\pmclsd{P}$ \\
+ $\pmast216\pmcdot04$. & $\pmperf{P}$ \\
+ $\pmast216\pmcdot05$. & $\pmders{P}$ \\
+ $\pmast230\pmcdot01$. & $\pmconv{R}{Q}{\alpha}$ \\
+ $\pmast230\pmcdot02$. & $\pmConv{Q}$
+\end{tabular}
+
+\begin{tabular}{l l}
+ $\pmast231\pmcdot01$. & $\pmlsc{P}{R}{Q}$ \\
+ $\pmast231\pmcdot02$. & $\pmosc{P}{R}{Q}$ \\
+ $\pmast232\pmcdot01$. & $\pmlscl{P}{R}{Q}{\alpha}$ \\
+ $\pmast232\pmcdot02$. & $\pmoscl{P}{R}{Q}{\alpha}$ \\
+ $\pmast233\pmcdot01$. & $\pmLmx{P}{R}{Q}$ \\
+ $\pmast233\pmcdot02$. & $\pmLimf{R}{P}{Q}$ \\
+ $\pmast234\pmcdot01$. & $\pmscf{P}{Q}{R}$ \\
+ $\pmast234\pmcdot02$. & $\pmosf{P}{Q}{R}$ \\
+ $\pmast234\pmcdot03$. & $\pmctf{P}{Q}{R}$ \\
+ $\pmast234\pmcdot04$. & $\pmcontinf{P}{Q}{R}$ \\
+ $\pmast234\pmcdot05$. & $\pmcontin{P}{Q}$ \\
+ $\pmast250\pmcdot01$. & $\pmbord$ \\
+ $\pmast250\pmcdot02$. & $\pmword$ \\
+ $\pmast251\pmcdot01$. & $\pmordn$ \\
+ $\pmast254\pmcdot01$. & $\pmLess$ \\
+ $\pmast254\pmcdot02$. & $\pmPsc$ \\
+ $\pmast255\pmcdot01$. & $\pmorle$ \\
+ $\pmast255\pmcdot02$. & $\pmorgr$ \\
+ $\pmast255\pmcdot03$. & $\pmnoo$ \\
+ $\pmast255\pmcdot04$. & $\pmorleq$ \\
+ $\pmast255\pmcdot05$. & $\pmorgrq$ \\
+ $\pmast255\pmcdot06$. & $\mu \pmorle \pmnr{P}$ \\
+ $\pmast255\pmcdot07$. & $\pmnr{P} \pmorle \mu$ \\
+ $\pmast256\pmcdot01$. & $\pmm$ \hspace{2ex} Dft [\(\pmast256\)] \\
+ $\pmast256\pmcdot02$. & $\pmn \,$ \hspace{2ex} Dft [\(\pmast256\)] \\
+ $\pmast257\pmcdot01$. & $\pmtranc{R}{Q}{x}$ \\
+ $\pmast257\pmcdot02$. & $\pmtrpot{Q}{R}{x}$ \\
+ $\pmast259\pmcdot01$. & $\pma$ \hspace{2.75ex} Dft [\(\pmast256\)] \\
+ $\pmast259\pmcdot02$. & $\pmaw$ \hspace{1.2ex} Dft [\(\pmast256\)] \\
+ $\pmast259\pmcdot03$. & $\pmwa$ \\
+ $\pmast260\pmcdot01$. & $\pmintf$ \\
+ $\pmast261\pmcdot01$. & $\pmserinf$
+\end{tabular}
+
+\begin{tabular}{l l}
+ $\pmast261\pmcdot02$. & $\pmwordinf$ \\
+ $\pmast261\pmcdot03$. & $\pmserfin$ \\
+ $\pmast261\pmcdot04$. & $\pmwordfin$ \\
+ $\pmast261\pmcdot05$. & $\pmwordind$ \\
+ $\pmast262\pmcdot01$. & $\pmordnfin$ \\
+ $\pmast262\pmcdot02$. & $\pmordninf$ \\
+ $\pmast262\pmcdot03$. & $\pmfinord{\mu}$ \\
+ $\pmast263\pmcdot01$. & $\pmom$ \\
+ $\pmast263\pmcdot02$. & $\pmn$ \hspace{3.4ex} Dft [\(\pmast263\)] \\
+ $\pmast264\pmcdot01$. & $\pmpr{P}$ \hspace{2ex} Dft [\(\pmast263\)] \\
+ $\pmast264\pmcdot429$. & $\pmrnprod{\pmrn{1}}{\alpha}$ \\
+ $\pmast265\pmcdot01$. & $\pmomn{1}$ \\
+ $\pmast265\pmcdot02$. & $\pmalephn{1}$ \\
+ $\pmast265\pmcdot03$. & $\pmomn{2}$ \\
+ $\pmast265\pmcdot04$. & $\pmalephn{2}$ \\
+ $\pmast265\pmcdot05$. & $\pmm$ \hspace{3.2ex} Dft [\(\pmast265\)] \\
+ $\pmast265\pmcdot06$. & $\pmn$ \hspace{3.5ex} Dft [\(\pmast265\)] \\
+ $\pmast270\pmcdot01$. & $\pmComp$ \\
+ $\pmast271\pmcdot01$. & $\pmmed$ \\
+ $\pmast272\pmcdot01$. & $\pmsimp{T}{P}{Q}$ \\
+ $\pmast273\pmcdot01$. & $\pmrats$ \\
+ $\pmast273\pmcdot02$. & $\pmsimps{R}{SPQ}{T}$ \hspace{3.4ex} Dft [\(\pmast273\)] \\
+ $\pmast273\pmcdot03$. & $\pmSimp{R}{S}{PQ}$ \hspace{3.5ex} Dft [\(\pmast273\)] \\
+ $\pmast273\pmcdot04$. & $\pmSimps{T}{RSPQ}$ \hspace{4.9ex} Dft [\(\pmast273\)] \\
+ $\pmast274\pmcdot01$. & $\pmsfcls{P}$ \\
+ $\pmast274\pmcdot02$. & $\pmsfclsm{P}{\kappa}$ \hspace{3.4ex} Dft [\(\pmast274\)] \\
+ $\pmast274\pmcdot03$. & $\pmsfclsp{T}{\kappa}$ \hspace{3.7ex} Dft [\(\pmast274\)] \\
+ $\pmast274\pmcdot04$. & $\pmsfclsmp{\kappa}$ \hspace{3ex} Dft [\(\pmast274\)] \\
+ $\pmast275\pmcdot01$. & $\pmcser$ \\
+ $\pmast276\pmcdot01$. & $\pmcsercl{P}$ \\
+ $\pmast276\pmcdot02$. & $\pma$ \hspace{7.3ex} Dft [\(\pmast276\)] \\
+ $\pmast276\pmcdot03$. & $\pmsfclsm{P}{\lambda}$ \hspace{4ex} Dft [\(\pmast276\)]
+\end{tabular}
+
+\begin{tabular}{l l}
+$\pmast276\pmcdot04$. & $\pmcsercls{T}{P}$ \hspace{8.2ex} Dft [\(\pmast276\)] \\
+$\pmast276\pmcdot05$. & $\pmCsercls{P}{\kappa}$ \hspace{6.25ex} Dft [\(\pmast276\)] \\
+$\pmast300\pmcdot01$. & $\pmu$ \\
+$\pmast300\pmcdot02$. & $\pmrnum$ \\
+$\pmast300\pmcdot03$. & $\pmrnumid$ \\
+$\pmast301\pmcdot01$. & $R_p$ \hspace{8.2ex} Dft [\(\pmast301\)] \\
+$\pmast301\pmcdot02$. & $\text{num}(R)$ \hspace{3ex} Dft [\(\pmast301\)] \\
+$\pmast301\pmcdot03$. & $\pmrpwr{R}{\sigma}$ \\
+$\pmast302\pmcdot01$. & $\pmPrm$ \\
+$\pmast302\pmcdot02$. & $\pmrprm{\rho}{\sigma}{\mu}{\nu}$ \\
+$\pmast302\pmcdot03$. & $\pmprm{\rho}{\sigma}{\mu}{\nu}$ \\
+$\pmast302\pmcdot04$. & $\pmhcf{\mu}{\nu}$ \\
+$\pmast302\pmcdot05$. & $\pmlcm{\mu}{\nu}$ \\
+$\pmast303\pmcdot01$. & $\pmrat{\mu}{\nu}$ \\
+$\pmast303\pmcdot02$. & $\pmqn{0}$ \\
+$\pmast303\pmcdot03$. & $\pmqnil$ \\
+$\pmast303\pmcdot04$. & $\pmRat$ \\
+$\pmast303\pmcdot05$. & $\pmRatdef$ \\
+$\pmast304\pmcdot01$. & $\pmqnle{X}{Y}$ \\
+$\pmast304\pmcdot02$. & $\pmqnLe$ \\
+$\pmast304\pmcdot03$. & $\pmqnlez$ \\
+$\pmast305\pmcdot01$. & $\pmprodsr{X}{Y}$ \\
+$\pmast306\pmcdot01$. & $\pmsumsr{X}{Y}$ \\
+$\pmast307\pmcdot01$. & $\pmratn$ \\
+$\pmast307\pmcdot011$. & $\pmratg$ \\
+$\pmast307\pmcdot02$. & $\pmRatnle$ \\
+$\pmast307\pmcdot021$. & $\pmRatngr$ \\
+$\pmast307\pmcdot03$. & $\pmRatgle$ \\
+$\pmast307\pmcdot031$. & $\pmRatggr$ \\
+$\pmast307\pmcdot04$. & $\pmratnLe$ \\
+$\pmast307\pmcdot05$. & $\pmratgLe$ \\
+$\pmast308\pmcdot01$. & $\pmratssub{X}{Y}$
+\end{tabular}
+
+\begin{tabular}{l l}
+$\pmast308\pmcdot02$. & $\pmsumgr{X}{Y}$ \\
+$\pmast309\pmcdot01$. & $\pmprodgr{X}{Y}$ \\
+$\pmast310\pmcdot01$. & $\pmrenp$ \\
+$\pmast310\pmcdot011$. & $\pmrenpz$ \\
+$\pmast310\pmcdot02$. & $\pmrenn$ \\
+$\pmast310\pmcdot021$. & $\pmrennz$ \\
+$\pmast310\pmcdot03$. & $\pmreng$ \\
+$\pmast311\pmcdot01$. & $\pmconc{\mu,\nu,...}$ \\
+$\pmast311\pmcdot02$. & $\pmrensumc{\mu}{\nu}$ \\
+$\pmast312\pmcdot01$. & $\pmrensub{\mu}{\nu}$ \\
+$\pmast312\pmcdot02$. & $\pmrensuma{\mu}{\nu}$ \\
+$\pmast313\pmcdot01$. & $\pmrenproda{\mu}{\nu}$ \\
+$\pmast314\pmcdot01$. & $\pmrenrsum{X}{Y}$ \\
+$\pmast314\pmcdot02$. & $\pmrenrprod{X}{Y}$ \\
+$\pmast314\pmcdot03$. & $\pmrenr$ \\
+$\pmast314\pmcdot04$. & $\pmrenrssum{M}{N}$ \\
+$\pmast314\pmcdot05$. & $\pmrenrsprod{M}{N}$ \\
+$\pmast330\pmcdot01$. & $\pmcr{\alpha}$ \\
+$\pmast330\pmcdot02$. & $\pmabel$ \\
+$\pmast330\pmcdot03$. & $\pmvfm{\alpha}$ \\
+$\pmast330\pmcdot04$. & $\pmvfmcl$ \\
+$\pmast330\pmcdot05$. & $\pmvffb{\kappa}$ \\
+$\pmast331\pmcdot01$. & $\pmconx{\kappa}$ \\
+$\pmast331\pmcdot02$. & $\pmconxfm$ \\
+$\pmast332\pmcdot01$. & $\pmfrep{\kappa}{P}$ \\
+$\pmast333\pmcdot01$. & $\pmfopen{\kappa}$ \\
+$\pmast333\pmcdot011$. & $\pmfopennid{\kappa}$ \\
+$\pmast333\pmcdot02$. & $\pmfmap$ \\
+$\pmast333\pmcdot03$. & $\pmfmapconx$
+\end{tabular}
+
+\begin{tabular}{l l}
+ $\pmast334\pmcdot01$. & $\pmtrsp{\kappa}$ \\
+ $\pmast334\pmcdot02$. & $\pmfmtrs$ \\
+ $\pmast334\pmcdot03$. & $\pmfmconnex$ \\
+ $\pmast334\pmcdot04$. & $\pmfmsr$ \\
+ $\pmast334\pmcdot05$. & $\pmfmasym$ \\
+ $\pmast335\pmcdot01$. & $\pminit{\kappa}$ \\
+ $\pmast335\pmcdot02$. & $\pmfminit$ \\
+ $\pmast336\pmcdot01$. & $\pmvr{\kappa}$ \\
+ $\pmast336\pmcdot011$. & $\pmvrnid{\kappa}$ \\
+ $\pmast336\pmcdot02$. & $\pmarvs{a}$ \\
+ $\pmast351\pmcdot01$. & $\pmfmsubm$ \\
+ $\pmast352\pmcdot01$. & $\pmvrm{T}{\kappa}$ \\
+ $\pmast352\pmcdot02$. & $\pmvrmg{T}{\kappa}$ \\
+ $\pmast353\pmcdot01$. & $\pmfmrt$ \\
+ $\pmast353\pmcdot02$. & $\pmfmcx$ \\
+ $\pmast353\pmcdot03$. & $\pmfmrtcx$ \\
+ $\pmast354\pmcdot01$. & $\pmfmg{\kappa}$ \\
+ $\pmast354\pmcdot02$. & $\pmrtnet{a}{\lambda}$ \\
+ $\pmast354\pmcdot03$. & $\pmfmgrp$ \\
+ $\pmast356\pmcdot01$. & $\pmrems{X}{\kappa}$ \\
+ $\pmast370\pmcdot01$. & $\pmfmcycl$ \\
+ $\pmast370\pmcdot02$. & $\pmcycl{K}{\kappa}$ \\
+ $\pmast370\pmcdot03$. & $\pmcycli{I}{\kappa}$ \\
+ $\pmast371\pmcdot01$. & $\pmvser{W}{\kappa}$ \\
+ $\pmast372\pmcdot01$. & $\pmintsecvser{\nu}{\kappa}$ \\
+ $\pmast373\pmcdot01$. & $\pmsfmid{M}{\nu}{\kappa}$ \hspace{2ex} Dft [\(\pmast373\text{---}5\)]\\
+ $\pmast373\pmcdot02$. & $\pmprime$ \\
+ $\pmast373\pmcdot03$. & $\pmsmltid{S}{\nu}$ \hspace{0.75ex} Dft [\(\pmast373\text{---}5\)]\\
+ $\pmast375\pmcdot01$. & $\pmprrt{\mu}{\nu}{\kappa}$
+\end{tabular}
+\end{document} \ No newline at end of file
diff --git a/macros/latex/contrib/principia/README b/macros/latex/contrib/principia/README
index 83b78ebc29..505f8978fd 100644
--- a/macros/latex/contrib/principia/README
+++ b/macros/latex/contrib/principia/README
@@ -1,12 +1,12 @@
principia.sty - a LaTeX2e package for typesetting the "Peanese" notation of Whitehead and Russell's 1910 "Principia Mathematica".
-The file principia.sty is the original work of Landon D. C. Elkind (Copyright (c) 2021). It is released under the LaTeX Project Public License 1.3c.
+The file principia.sty is the original work of Landon D. C. Elkind (Copyright (c) 2023). It is released under the LaTeX Project Public License 1.3c.
-This is principia package Version 1.3 (2021/04/19). This version covers typesetting the notations through Sections A and B in Volume I of "Principia Mathematica". See the file principia.pdf for information on these changes and for further information on how to typeset Peanese symbols in LaTeX with the principia package.
+This is principia package Version 2.0 (2023/03/13). This version covers typesetting the notations through Volumes I-III of "Principia Mathematica". See the file principia.pdf for information on these changes and for further information on how to typeset Peanese symbols in LaTeX with the principia package.
Changes between version updates can be found at https://logicalatomist.github.io/principia/
Comments and suggestions are welcomed by the package maintainer, signed below.
Landon D. C. Elkind
-University of Alberta
+Western Kentucky University
diff --git a/macros/latex/contrib/principia/principia.pdf b/macros/latex/contrib/principia/principia.pdf
index b0c8da5020..87c69193ba 100644
--- a/macros/latex/contrib/principia/principia.pdf
+++ b/macros/latex/contrib/principia/principia.pdf
Binary files differ
diff --git a/macros/latex/contrib/principia/principia.sty b/macros/latex/contrib/principia/principia.sty
index 421a0b65ab..29591fc070 100644
--- a/macros/latex/contrib/principia/principia.sty
+++ b/macros/latex/contrib/principia/principia.sty
@@ -1,13 +1,13 @@
%Package Identification
\NeedsTeXFormat{LaTeX2e}
-\ProvidesPackage{principia}[2021/04/19 principia package version 1.3] %This is the principia package is for representing notations in Whitehead and Russell's ``Principia Mathematica" close to their appearance in the original.
+\ProvidesPackage{principia}[2023/03/13 principia package version 2.0] %This is the principia package is for representing notations in Whitehead and Russell's ``Principia Mathematica" close to their appearance in the original.
%Version 1.0 (superseded by Version 1.1): Covers typesetting of notation through Volume I. 2020/10/24
%Version 1.1 (superseded by Version 1.2) minor updates: fixed the spacing of scope dots around parentheses; fixed spacing of theorem sign; fixed spacing around primitive proposition and definition signs. 2020/10/25
%Licensed under LaTeX Project Public License 1.3c.
-%Version 1.2 (superseded by Version 1.3) (minor updates): boldfaced (`thickened') the truth-functional connectives, existential quantifier, set and relation symbols; added numerous commands for typesetting brackets and substitutions into theorems. 2021/02/25
-%Version 1.3 (minor update): removes package dependency on marvosym; updates Section A notation; removes other notations (corrected extension pending). 2021/04/19
+%Version 1.2 (superseded by Version 2.0) (minor updates): boldfaced (`thickened') the truth-functional connectives, existential quantifier, set and relation symbols; added numerous commands for typesetting brackets and substitutions into theorems. 2021/02/25
+%Version 2.0 (major update): extends the package to cover typesetting of all notations in Volumes II and III; removes package dependency on marvosym. 2022/09/04
%Licensed under LaTeX Project Public License 1.3c.
-%Copyright Landon D. C. Elkind, 2021 (https://landondcelkind.com/contact/).
+%Copyright Landon D. C. Elkind, 2023 (https://landonelkind.com/contact/).
%Principia package requirements
\RequirePackage{amssymb} %This loads the relation domain and converse domain limitation symbols.
@@ -20,6 +20,26 @@
%Mathematical logic
%The theory of deduction
%Meta-logical symbols
+\newcommand{\ie}{\textit{i}.\textit{e}.\ }
+\newcommand{\Ie}{\textit{I}.\textit{e}.\ }
+\newcommand{\eg}{\textit{e}.\textit{g}.\ }
+\newcommand{\Eg}{\textit{E}.\textit{g}.\ }
+\newcommand{\pmsch}[1]{\pmast#1} %Starred chapter
+\newcommand{\pmschs}[2]{\pmast#1\text{---}\pmast#2} %Starred chapter
+\newcommand{\pmsns}[3]{\pmast#1\pmcdot#2\text{---}\pmcdot#3}%Starred number
+\newcommand{\pmpsn}[2]{(\pmast#1\pmcdot#2)}
+\newcommand{\pmpsnn}[3]{(\pmast#1\pmcdot#2\pmcdot#3)}
+\newcommand{\pmsn}[2]{\pmast#1\pmcdot#2}
+\newcommand{\pmnsn}[1]{\text{#1}}
+\newcommand{\pmsnn}[3]{\pmast#1\pmcdot#2\pmcdot#3}
+\newcommand{\pmsnnn}[4]{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4}
+\newcommand{\pmsnnnn}[5]{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5}
+\newcommand{\pmsnnnnn}[6]{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5\pmcdot#6}
+\newcommand{\pmsnb}[2]{\boldsymbol{\pmast#1\pmcdot#2}} %Starred number boldface
+\newcommand{\pmsnnb}[3]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3}}
+\newcommand{\pmsnnnb}[4]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4}}
+\newcommand{\pmsnnnnb}[5]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5}}
+\newcommand{\pmsnnnnnb}[6]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5\pmcdot#6}}
\newcommand{\pmfd}{\begin{center} \rule{5cm}{.5pt} \end{center}} %Dividing line between introductory remarks in a starred number and the formal deductions.
\newcommand{\pmdem}{\textit{Dem}.} %This notation begins a proof.
\newcommand{\pmdemi}{\indent \pmdem} %This idents the notation that begins a proof.
@@ -34,7 +54,7 @@
\newcommand{\pmSub}[3]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array} \bigg \rbrack} %This is the substitution command.
\newcommand{\pmSubb}[5]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array} \bigg \rbrack} %This is the substitution command.
\newcommand{\pmSubbb}[7]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array} \bigg \rbrack} %This is the substitution command.
-\newcommand{\pmSubbbb}[9]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array} \bigg \rbrack} %This is the substitution command.
+\newcommand{\pmSubbbb}[9]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c c} #2, & #4, & #6, & #8 \\ \hline #3, & #5, & #7, & #9 \end{array} \bigg \rbrack} %This is the substitution command.
\newcommand{\pmsUb}[2]{\small \begin{array}{c} #1 \\ \hline #2 \end{array}} %This is the substitution command.
\newcommand{\pmsUbb}[4]{\small \begin{array}{c c} #1, & #3 \\ \hline #2, & #4 \end{array}} %This is the substitution command.
\newcommand{\pmsUbbb}[6]{\small \begin{array}{c c c} #1, & #3, & #5 \\ \hline #2, & #4, & #6 \end{array}} %This is the substitution command.
@@ -42,12 +62,13 @@
\newcommand{\pmSUb}[3]{\normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array}} %This is the substitution command.
\newcommand{\pmSUbb}[5]{\normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array}} %This is the substitution command.
\newcommand{\pmSUbbb}[7]{\normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array}} %This is the substitution command.
-\newcommand{\pmSUbbbb}[9]{\normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}} %This is the substitution command.
+\newcommand{\pmSUbbbb}[9]{\normalsize #1 \text{ } \small \begin{array}{c c c c} #2, & #4, & #6, & #8 \\ \hline #3, & #5, & #7, & #9 \end{array}} %This is the substitution command.
\newcommand{\pmthm}{\mathpunct{\text{\scalebox{.5}[1]{$\boldsymbol\vdash$}}}} %This is the theorem sign.
\newcommand{\pmast}{\text{\resizebox{!}{.75\height}{\ding{107}}}} %This is the sign introducing a theorem number.
\newcommand{\pmcdot}{\text{\raisebox{.05cm}{$\boldsymbol\cdot$}}} %This is a sign introducing a theorem sub-number.
\newcommand{\pmiddf}{\mathbin{=}}
\newcommand{\pmdf}{\quad \text{Df}}
+\newcommand{\pmDf}{\text{Df}}
\newcommand{\pmpp}{\quad \text{Pp}}
%Square dots for scope, defined for up to six dots
@@ -70,6 +91,7 @@
\newcommand{\pmandddddd}{\pmandd\hspace{.1em}\pmandd\hspace{.1em}\pmandd}
\newcommand{\pmprod}{\mathbin{\ooalign{$\boldsymbol{\wedge}\mkern.5mu$\hidewidth\cr$\boldsymbol{\wedge}$\cr\hidewidth$\mkern.5mu\boldsymbol{\wedge}$}}} %Not in Principia, but added here as a dual of its symbol for disjunction.
\newcommand{\pmiff}{\mathbin{\ooalign{$\boldsymbol{\equiv}\mkern.5mu$\hidewidth\cr$\boldsymbol{\equiv}$\cr\hidewidth$\mkern.5mu\boldsymbol{\equiv}$}}} %4.01
+\newcommand{\pminc}{\mathbin{|}} %8.01
%The theory of apparent variables
\newcommand{\pmall}[1]{(#1)}
@@ -77,18 +99,568 @@
\newcommand{\pmSome}{\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}}
%Additional defined logic signs
-\newcommand{\pmhat}[1]{\mathbf{\hat{\text{$#1$}}}}
-\newcommand{\pmbreve}[1]{\mathbf{\breve{\text{$#1$}}}}
-\newcommand{\pmcirc}[1]{\mathbf{\dot{\text{$#1$}}}}
+\newcommand{\pmhat}[1]{\boldsymbol{\hat{\text{$#1$}}}}
+\newcommand{\pmbreve}[1]{\boldsymbol{\breve{\text{$#1$}}}}
+\newcommand{\pmcirc}[1]{\boldsymbol{\dot{\text{$#1$}}}}
\newcommand{\pmpf}[2]{#1#2} %for propositional functions of one variable
\newcommand{\pmpff}[3]{#1(#2, #3)} %for propositional functions of two variables
\newcommand{\pmpfff}[4]{#1(#2, #3, #4)} %for propositional functions of three variables
+\newcommand{\pmpffff}[5]{#1(#2, #3, #4, #5)} %for propositional functions of four variables (including ellipses)
+\newcommand{\pmppf}[2]{#1\pmshr#2} %for propositional predicative functions of one variable
+\newcommand{\pmppff}[3]{#1\pmshr(#2, #3)} %for propositional predicative functions of two variables
\newcommand{\pmshr}{\textbf{!}} %*12.1 and *12.11, used for predicative propositional functions
\newcommand{\pmpred}[2]{#1\pmshr#2} %for predicates (``predicative functions'') of one variable
\newcommand{\pmpredd}[3]{#1\pmshr(#2, #3)} %for predicates (``predicative functions'') of two variables
\newcommand{\pmpreddd}[4]{#1\pmshr(#2, #3, #4)} %for predicates (``predicative functions'') of three variables
+\newcommand{\pmpredddd}[5]{#1\pmshr(#2, #3, #4, #5)} %for predicates (``predicative functions'') of four variables
+\newcommand{\pmpreddddd}[6]{#1\pmshr(#2, #3, #4, #5, #6)} %for predicates (``predicative functions'') of five variables
+\newcommand{\pmpredddddd}[7]{#1\pmshr(#2, #3, #4, #5, #6, #7)} %for predicates (``predicative functions'') of six variables
+\newcommand{\pmid}{\mathbin{=}}
\newcommand{\pmnid}{\mathrel{\ooalign{$=$\cr\hidewidth\footnotesize\rotatebox[origin=c]{210}{\textbf{/}}\hidewidth\cr}}} %*13.02
-\newcommand{\pmiota}{\ooalign{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}\cr\hidewidth\raisebox{.0125em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.025em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.0375em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.05em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}}} %the rotated Greek iota used in definite descriptions
+\newcommand{\pmiota}{\ooalign{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}\cr\hidewidth\raisebox{.0125em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}\cr\hidewidth\raisebox{.025em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}\cr\hidewidth\raisebox{.0375em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}\cr\hidewidth\raisebox{.05em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}}} %the rotated Greek iota used in definite descriptions
\newcommand{\pmdsc}[1]{(\pmiota#1)} %*14.01
+\newcommand{\pmthe}[2]{(\pmiota#1)(#2 #1)} %*14.01
+\newcommand{\pmtheb}[2]{[(\pmiota#1)(#2 #1)]} %*14.01
\newcommand{\pmDsc}{\pmiota}
-\newcommand{\pmexists}{\textbf{E}\hspace{.1em}\pmshr} %*14.02 \ No newline at end of file
+\newcommand{\pmexists}{\textbf{E}\hspace{.1em}\pmshr} %*14.02
+
+%Classes and relations
+%Class signs
+\newcommand{\pmcls}[2]{\pmhat{#1}(#2)} %20.01
+\newcommand{\pmcin}{\mathop{\boldsymbol{\epsilon}}} %20.02
+\newcommand{\pmCls}{\text{Cls}} %20.03
+\newcommand{\pmClsn}[1]{\text{Cls}^{#1}}
+\newcommand{\pmcinn}{\pmnot\pmcin} %20.06
+\newcommand{\pmcinc}{\mathop{\ooalign{$\boldsymbol{\subset}$\cr\hidewidth$\hspace{.1em}\boldsymbol{\subset}$\cr\hidewidth$\hspace{.15em}\boldsymbol{\subset}$\cr\hidewidth$\hspace{.2em}\boldsymbol{\subset}$}}} %22.01
+\newcommand{\pmccap}{\mathop{\ooalign{\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.1em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.2em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.3em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.4em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.5em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.6em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}}}} %22.02
+\newcommand{\pmccup}{\mathop{\ooalign{\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.1em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.2em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.3em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.4em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.5em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.6em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}}}} %22.03
+\newcommand{\pmccmp}[1]{\boldsymbol{-}#1} %22.04
+\newcommand{\pmcmin}[2]{#1\boldsymbol{-}#2} %22.05
+\newcommand{\pmcuni}{\text{\rotatebox[origin=c]{180}{$\Lambda$}}} %24.01
+\newcommand{\pmcnull}{\Lambda} %24.02
+\newcommand{\pmcexists}{\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}\hspace{-.1em}\mathop{\pmshr}} %24.03
+
+%Relation signs
+\newcommand{\pmrel}[3]{\pmhat{#1}\pmhat{#2}#3} %21.01
+\newcommand{\pmrele}[5]{#1\{\pmhat{#2}\pmhat{#3}#4(#2, #3)\}#5} %21.02
+\newcommand{\pmrelep}[3]{#1\{#2\}#3} %21.08, 21.081, 21.082, etc.
+\newcommand{\pmrcmp}[1]{\ooalign{$\hidewidth\raisebox{.25em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccmp}$}#1} %23.04
+\newcommand{\pmrmin}[2]{#1\mathrel{\ooalign{$\hidewidth\raisebox{.25em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccmp}$}}#2} %23.05
+\newcommand{\pmruni}{\pmcirc{\text{\rotatebox[origin=c]{180}{$\Lambda$}}}} %25.01
+\newcommand{\pmrnull}{\pmcirc{\Lambda}} %25.02
+\newcommand{\pmrexists}{\pmcirc{\mathop{\text{\raisebox{.5em}{\rotatebox{180}{E}}}}}\mathop{\pmshr}} %25.03
+\newcommand{\pmrinc}{\mathrel{\ooalign{$\hidewidth\boldsymbol{\cdot}\hidewidth$\cr$\boldsymbol{\pmcinc}$}}} %23.01
+\newcommand{\pmrcap}{\mathrel{\ooalign{$\hidewidth\raisebox{.3em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccap}$}}} %23.02
+\newcommand{\pmrcup}{\mathrel{\ooalign{$\hidewidth\raisebox{.1em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccup}$}}} %23.03
+
+%Logic of Relations
+\newcommand{\pmdscf}[2]{#1\textbf{`}#2} %30.01
+\newcommand{\pmcnv}[1]{\text{Cnv}\textbf{`}#1} %31.01
+\newcommand{\pmCnv}{\text{Cnv}}
+\newcommand{\pmcrel}[1]{\pmbreve{#1}} %31.02
+\newcommand{\pmrrf}[2]{\overset{\boldsymbol{\rightarrow}}{#1\textbf{`}}#2} %32.01
+\newcommand{\pmRrf}[1]{\overset{\boldsymbol{\rightarrow}}{#1}}
+\newcommand{\pmrrl}[2]{\overset{\boldsymbol{\leftarrow}}{#1\textbf{`}}#2} %32.02
+\newcommand{\pmRrl}[1]{\overset{\boldsymbol{\leftarrow}}{#1}}
+\newcommand{\pmsg}[1]{\text{sg}\textbf{`}#1} %32.03
+\newcommand{\pmSg}{\text{sg}}
+\newcommand{\pmgs}[1]{\text{gs}\textbf{`}#1} %32.04
+\newcommand{\pmGs}{\text{gs}}
+\newcommand{\pmdm}[1]{\text{D}\textbf{`}#1} %33.01
+\newcommand{\pmDm}{\text{D}}
+\newcommand{\pmcdm}[1]{\text{\rotatebox[origin=c]{180}{D}}\textbf{`}#1} %33.02
+\newcommand{\pmCdm}{\text{\rotatebox[origin=c]{180}{D}}}
+\newcommand{\pmcmp}[1]{C\textbf{`}#1} %33.03
+\newcommand{\pmCmp}{C}
+\newcommand{\pmfld}[1]{F\textbf{`}#1} %33.04
+\newcommand{\pmFld}{F}
+\newcommand{\pmrprd}[2]{{#1}\mathop{|}{#2}} %34.01
+\newcommand{\pmRprd}{\mathop{|}}
+\newcommand{\pmrprdn}[2]{#1^{#2}} %34.02, 34.03, etc.
+\newcommand{\pmrld}[2]{#1 \boldsymbol{\upharpoonleft} #2} %35.01
+\newcommand{\pmrlcd}[2]{#1 \boldsymbol{\upharpoonright} #2} %35.02
+\newcommand{\pmrlf}[3]{#1 \boldsymbol{\upharpoonleft} #2 \boldsymbol{\upharpoonright} #3} %35.03
+\newcommand{\pmrl}[2]{#1 \boldsymbol{\uparrow} #2} %35.04
+\newcommand{\pmrlF}[2]{#1 \mathbin{\ooalign{$\upharpoonright$\cr\hidewidth\rotatebox[origin=c]{180}{\text{$\upharpoonleft$}}\hidewidth\cr}} #2} %36.01
+\newcommand{\pmdscff}[2]{#1\textbf{`}\textbf{`}#2} %37.01
+\newcommand{\pmdscfr}[2]{#1_{\pmcin}\textbf{`}#2} %37.02
+\newcommand{\pmdscfR}[1]{#1_{\pmcin}}
+\newcommand{\pmdscfcr}[2]{\pmbreve{#1}_{\pmcin}\textbf{`}#2} %37.03
+\newcommand{\pmdscfcR}[1]{\pmbreve{#1}_{\pmcin}}
+\newcommand{\pmdscfff}[2]{#1\textbf{`}\textbf{`}\textbf{`}#2} %37.04
+\newcommand{\pmdscfe}[2]{\mathop{\text{E}}\mathop{\pmshr\pmshr}\pmdscff{#1}{#2}} %37.05
+\newcommand{\Female}{{\usefont{U}{mvs}{m}{n}\symbol{126}}} %from the Marvosym package
+\newcommand{\pmop}{\mathop{\text{\Female}}} %38.01, 38.02
+\newcommand{\pmopc}[2]{#1 \mathop{\underset{\textbf{''}}{\text{\Female}}} #2} %38.03
+
+%Products and sums of classes of classes or relations
+\newcommand{\pmccsum}[1]{p\textbf{`}#1} %40.01
+\newcommand{\pmccprd}[1]{s\textbf{`}#1} %40.02
+\newcommand{\pmcrsum}[1]{\pmcirc{p}\textbf{`}#1} %41.01
+\newcommand{\pmcrprd}[1]{\pmcirc{s}\textbf{`}#1} %41.02
+\newcommand{\pmrprdd}[2]{{#1}\mathop{||}{#2}} %43.01
+\newcommand{\pmRprdd}{\mathop{||}}
+
+%Prolegomena to Cardinal Arithmetic
+%Unit Classes and Couples
+%Identity and Diversity
+\newcommand{\pmrid}{I} %50.01
+\newcommand{\pmrdiv}{J} %50.02
+\newcommand{\pmcunit}[1]{\iota\textbf{`}#1} %51.01
+\newcommand{\pmcUnit}{\iota}
+\newcommand{\pmcunits}[1]{\pmbreve{\iota}\textbf{`}#1} %52.01
+
+%Cardinal numbers
+\newcommand{\pmcn}[1]{#1} %52.01, 54.01, 54.02, etc.
+
+%Ordinal numbers
+\newcommand{\pmoc}[2]{#1 \boldsymbol{\downarrow} #2} %55.01, 55.02, etc.
+\newcommand{\pmdn}[1]{\pmcirc{#1}} %56.01
+\newcommand{\pmorn}[1]{#1_r} %56.02, 56.03, etc.
+
+%Sub-classes, Sub-relations, and Relative Types
+%Sub-classes
+\newcommand{\pmscl}[1]{\text{Cl}\textbf{`}#1} %60.01
+\newcommand{\pmsCl}{\text{Cl}}
+\newcommand{\pmscle}[1]{\text{Cl ex}\textbf{`}#1} %60.02
+\newcommand{\pmsCle}{\text{Cl ex}}
+\newcommand{\pmscls}[1]{\text{Cls}\textbf{`}#1} %60.03
+\newcommand{\pmsrl}[1]{\text{Rl}\textbf{`}#1} %61.01
+\newcommand{\pmsRl}{\text{Rl}}
+\newcommand{\pmsrle}[1]{\text{Rl ex}\textbf{`}#1} %61.02
+\newcommand{\pmsRle}{\text{Rl ex}}
+\newcommand{\pmsrel}[1]{\text{Rel}\textbf{`}#1} %61.03
+\newcommand{\pmRel}{\text{Rel}}
+\newcommand{\pmReln}[1]{\text{Rel}^{#1}} %61.04
+\newcommand{\pmrin}{\mathop{\boldsymbol{\epsilon}}} %62.01
+
+%Relative type symbols
+\newcommand{\pmrt}[1]{t\textbf{`}#1} %63.01
+\newcommand{\pmrti}[2]{t^{#1}\textbf{`}#2} %63.011
+\newcommand{\pmrtc}[2]{t_{#1}\textbf{`}#2} %63.02, 63.03, etc.
+\newcommand{\pmrtri}[2]{t^{#1}\textbf{`}#2} %63.04
+\newcommand{\pmrtrc}[2]{t_{#1}\textbf{`}#2} %64.02, 64.021, 64.022, etc.
+\newcommand{\pmrtrci}[3]{t_{#1}^{\text{ }#2}\textbf{`}#3} %64.03, 64.031, etc.
+\newcommand{\pmrtric}[3]{{}^{#1}t_{#2}\textbf{`}#3} %64.04, 64.041, etc.
+\newcommand{\pmrtdi}[2]{#1_{#2}} %65.01
+\newcommand{\pmrtdc}[2]{#1(#2)} %65.02
+\newcommand{\pmrtdri}[2]{#1_{#2}} %65.03
+\newcommand{\pmrtdrc}[2]{#1(#2)} %65.04
+
+%One-many, Many-one, and One-one relations
+%Similarity relation signs
+\newcommand{\pmrdc}[2]{#1\boldsymbol{\to}#2} %70.01
+\newcommand{\pmsmbar}{\mathrel{\overline{\text{sm}}}} %73.01
+\newcommand{\pmsm}{\mathrel{\text{sm}}} %73.02
+\newcommand{\pmSM}{\text{sm}}
+\newcommand{\pmsmarr}{\overrightarrow{{\pmsm}}}
+\newcommand{\pmonemany}{1\boldsymbol{\to}\pmCls}
+\newcommand{\pmmanyone}{\pmCls\boldsymbol{\to}1}
+\newcommand{\pmoneone}{1\boldsymbol{\to}1}
+
+%Selections
+\newcommand{\pmselp}[1]{P_{\small\Delta}\boldsymbol{`}#1} %80.01
+\newcommand{\pmSelp}{P_{\Delta}}
+\newcommand{\pmsele}[1]{\pmcin_{\small\Delta}\boldsymbol{`}#1}
+\newcommand{\pmSele}{\pmcin_{\Delta}}
+\newcommand{\pmself}[1]{F_{\small\Delta}\boldsymbol{`}#1}
+\newcommand{\pmSelf}{F_{\Delta}}
+\newcommand{\pmexc}{\text{Cls}^2 \mathop{\text{excl}}} %84.01
+\newcommand{\pmexcc}[1]{\text{Cl} \mathop{\text{excl}}\textbf{`}#1} %84.02
+\newcommand{\pmex}{\text{Cls excl}}
+\newcommand{\pmexcn}{\text{Cls} \mathop{\text{ex}^2} \mathop{\text{excl}}} %84.03
+\newcommand{\pmselc}[2]{#1 \mathrel{\ooalign{\rotatebox[origin=c]{270}{$\boldsymbol{\mapsto}$}}} #2}
+\newcommand{\pmmultr}{\mathop{\text{Rel}} \mathop{\text{Mult}}} %88.01
+\newcommand{\pmmultc}{\mathop{\text{Cls}^2} \mathop{\text{Mult}}} %88.02
+\newcommand{\pmmultax}{\mathop{\text{Mult}} \mathop{\text{ax}}} %88.03
+
+%Inductive relations
+\newcommand{\pmanc}[1]{#1_\pmast} %90.01
+\newcommand{\pmancc}[1]{\pmcrel{#1}_\pmast} %90.02
+\newcommand{\pmrst}[1]{#1_\text{st}} %91.01
+\newcommand{\pmrts}[1]{#1_\text{ts}} %91.02
+\newcommand{\pmpot}[1]{\text{Pot}\boldsymbol{`}#1} %91.03
+\newcommand{\pmpotid}[1]{\text{Potid}\boldsymbol{`}#1} %91.04
+\newcommand{\pmpo}[1]{#1_\text{po}} %91.05
+\newcommand{\pmB}{B} %93.01
+\newcommand{\pmmin}[1]{\text{min}_{#1}} %93.02
+\newcommand{\pmMin}{\text{min}}
+\newcommand{\pmmax}[1]{\text{max}_{#1}} %93.021
+\newcommand{\pmMax}{\text{max}}
+\newcommand{\pmgen}[1]{\text{gen}\boldsymbol{`}#1} %93.03
+\newcommand{\pmGen}{\text{gen}}
+\newcommand{\pmefr}[2]{#1\pmast#2} %95.05
+\newcommand{\pmipr}[2]{I_{#1}\textbf{`}#2} %96.01
+\newcommand{\pmjpr}[2]{J_{#1}\textbf{`}#2} %96.02
+\newcommand{\pmfr}[2]{\overset{\boldsymbol{\leftrightarrow}}{#1}\textbf{`}#2} %97.01
+
+%Volume II
+%Cardinal arithmetic
+%Definition and Logical Properties of Cardinal Numbers
+\newcommand{\pmnc}[1]{\text{Nc}\textbf{`}#1} %100.01
+\newcommand{\pmNc}{\text{Nc}}
+\newcommand{\pmNC}{\text{NC}} %100.02
+\newcommand{\pmNCat}[2]{\text{NC}^{#1}({#2})} %102.01
+\newcommand{\pmnoc}[1]{\text{N}_0\text{c}\textbf{`}#1} %103.01
+\newcommand{\pmNoc}{\text{N}_0\text{c}}
+\newcommand{\pmNoC}{\text{N}_0\text{C}} %103.02
+\newcommand{\pmnca}[2]{\text{N}^{#1}\text{c}\textbf{`}#2} %104.01, 104.011, etc.
+\newcommand{\pmNca}[1]{\text{N}^{#1}\text{C}} %104.02, 104.021, etc.
+\newcommand{\pmch}[2]{#1^{(#2)}} %104.03, 104.031, etc.
+\newcommand{\pmncd}[2]{\text{N}_{#1}\text{c}\textbf{`}#2} %105.01
+\newcommand{\pmNcd}[1]{\text{N}_{#1}\text{C}} %105.02, 105.021, etc.
+\newcommand{\pmcl}[2]{#1_{(#2)}} %105.03, 105.031, etc.
+\newcommand{\pmncll}[3]{\text{N}_{#1#2}\text{c}\textbf{`}#3} %106.01, 106.012, etc.
+\newcommand{\pmnchh}[3]{\text{N}^{#1#2}\text{c}\textbf{`}#3} %106.011
+\newcommand{\pmncaa}[3]{\text{N}_{#1}{}^{#2}\text{c}\textbf{`}#3} %106.02
+\newcommand{\pmncdd}[3]{{}^{#1}\text{N}_{#2}\text{c}\textbf{`}#3} %106.021
+\newcommand{\pmNCll}[2]{\text{N}_{#1#2}\text{C}} %106.03
+\newcommand{\pmNChh}[2]{\text{N}^{#1#2}\text{C}}
+\newcommand{\pmcll}[3]{#1_{(#2#3)}} %106.04
+\newcommand{\pmchh}[3]{#1^{(#2#3)}} %106.041
+\newcommand{\pmncr}[1]{\text{N}_{00}\text{c}\textbf{`}#1} %106.01
+
+%Addition, Multiplication, Exponentiation
+\newcommand{\pmarsumc}{\mathrel{+}} %110.01
+\newcommand{\pmarsumnc}{\mathrel{{+}_{\text{c}}}} %110.02
+\newcommand{\pmsmsmb}{\mathrel{\overline{\text{sm}}\;\overline{\text{sm}}}} %111.01
+\newcommand{\pmcrp}[2]{\text{Crp}(#1)\textbf{`}#2} %111.02
+\newcommand{\pmsmsm}{\mathrel{\text{sm}\;\text{sm}}} %111.03
+\newcommand{\pmarsumcc}[1]{\Sigma\textbf{`}#1} %112.01
+\newcommand{\pmarsumcnc}[1]{\Sigma\pmNc\textbf{`}#1} %112.02
+\newcommand{\pmarprodc}{\times} %113.02
+\newcommand{\pmarprodnc}{\times_\text{c}} %113.03
+\newcommand{\pmarprodcnc}[1]{\Pi\pmNc\textbf{`}#1} %114.01
+\newcommand{\pmarprodcc}[1]{\text{Prod}\textbf{`}#1} %115.01
+\newcommand{\pmarcls}{\pmClsn{3}\text{arithm}} %115.02
+\newcommand{\pmarexp}[2]{#1 \mathrel{\text{exp}} #2} %116.01
+\newcommand{\pmArexp}{\text{exp}}
+\newcommand{\pmarncexp}[2]{#1^{#2}} %116.02
+\newcommand{\pmarg}{\mathrel{\boldsymbol{>}}} %117.01
+\newcommand{\pmarl}{\mathrel{\boldsymbol{<}}} %117.04
+\newcommand{\pmargeq}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr${\hspace{-.4ex}\raise-.75ex\hbox{\rotatebox[origin=c]{-155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}$}}} %117.05
+\newcommand{\pmarleq}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth${\raise-.75ex\hbox{\rotatebox[origin=c]{155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}\hspace{-.375ex}$}}} %117.06
+
+%Finite and infinite
+\newcommand{\pmarsubt}[2]{#1 \mathrel{{-}_\text{c}} #2} %119.01
+\newcommand{\pmArsubt}{{-}_\text{c}}
+\newcommand{\pmNCinduct}{\text{NC}\,\text{induct}} %120.01
+\newcommand{\pmncinduct}[1]{\text{N}_#1\text{C}\,\text{induct}} %120.011
+\newcommand{\pmClsinduct}{\text{Cls}\,\text{induct}} %120.02
+\newcommand{\pmclsinduct}[1]{\text{Cls}_{#1}\,\text{induct}} %120.021
+\newcommand{\pmInfinax}{\text{Infin}\,\text{ax}} %120.03
+\newcommand{\pminfinax}[1]{\text{Infin}\,\text{ax}(#1)} %120.04
+\newcommand{\pmspec}[1]{\text{spec}\textbf{`}#1} %120.43
+\newcommand{\pmintoo}[2]{P(#1\mathbin{\boldsymbol{-}}#2)} %121.01
+\newcommand{\pmintoc}[2]{P({#1}\mathbin{\scalebox{1.2}[.7]{$\boldsymbol{\dashv}$}}{#2})} %121.011
+\newcommand{\pmintco}[2]{P({#1}\mathbin{\scalebox{1.2}[.7]{$\boldsymbol{\vdash}$}}{#2})} %121.012
+\newcommand{\pmintcc}[2]{P({#1} \mathbin{\ooalign{$\scalebox{1.2}[.7]{$\boldsymbol{\dashv}$}$\hidewidth\cr$\scalebox{1.2}[.7]{$\boldsymbol{\vdash}$}$}} {#2})} %121.013
+\newcommand{\pmintnc}[1]{P_{#1}} %121.02
+\newcommand{\pmfinid}[1]{\text{finid}\textbf{`}#1} %121.03
+\newcommand{\pmfin}[1]{\text{fin}\textbf{`}#1} %121.031
+\newcommand{\pmintt}[2]{#1_{#2}} %121.04
+\newcommand{\pmprog}{\text{Prog}} %122.01
+\newcommand{\pmaleph}{\boldsymbol{\aleph}} %123.01
+\newcommand{\pmsucc}{\text{N}} %123.02
+\newcommand{\pmclsrefl}{\text{Cls}\;\text{refl}} %124.01
+\newcommand{\pmncrefl}{\text{NC}\;\text{refl}} %124.02
+\newcommand{\pmncmult}{\text{NC}\;\text{mult}} %124.03
+\newcommand{\pmncind}{\text{NC}\;\text{ind}} %126.01
+\newcommand{\pmnocind}[1]{\text{N}_0\text{Cinduct}\textbf{`}#1}
+\newcommand{\pmNocind}{\text{N}_0\text{Cinduct}}
+
+%Relation-arithmetic
+%Ordinal similarity and relation-numbers
+\newcommand{\pmrnsm}[2]{{#1}{\raise.4ex\hbox{\textbf{\large;}}}{#2}} %150.01
+\newcommand{\pmrnsmd}[2]{#1 \mathop{\boldsymbol{\dagger}} #2} %150.02
+\newcommand{\pmrnsmdf}[1]{#1\boldsymbol{\dagger}}
+\newcommand{\pmopsc}[2]{#1 \mathrel{\ooalign{${\raise-.7ex\hbox{$\pmdot$}}$\hidewidth\cr$\text{\Female}$\hidewidth\cr${\raise-.8ex\hbox{\hspace{.15cm}\textbf{,}}}$}} #2} %150.03
+\newcommand{\pmsmorb}[2]{#1 \mathrel{\overline{\text{smor}}} #2} %151.01
+\newcommand{\pmSmorb}{\overline{\text{smor}}} %151.01
+\newcommand{\pmsmor}[2]{#1 \mathrel{\text{smor}} #2} %151.02
+\newcommand{\pmSmor}{\text{smor}}
+\newcommand{\pmnr}[1]{\text{Nr}\textbf{`}#1} %152.01
+\newcommand{\pmNr}{\text{Nr}}
+\newcommand{\pmNR}{\text{NR}} %152.02
+\newcommand{\pmsrrn}[1]{{#1}_{s}} %153.01
+\newcommand{\pmNRat}[2]{\text{NR}^{#1}({#2})} %154.01
+\newcommand{\pmnor}[1]{\text{N}_0\text{r}\textbf{`}#1} %155.01
+\newcommand{\pmNor}{\text{N}_0\text{r}}
+\newcommand{\pmNoR}{\text{N}_0\text{R}} %155.02
+
+%Addition of Relations, and the Product of Two Relations
+\newcommand{\pmrsum}[2]{#1\mathrel{\ooalign{${\raise-.21ex\hbox{$\boldsymbol{-}$}}$\cr\hidewidth$\boldsymbol{\uparrow}$\hidewidth\cr${\raise-.19ex\hbox{$\boldsymbol{-}$}}$}} #2} %160.01
+\newcommand{\pmRsum}{\mathrel{\ooalign{${\raise-.21ex\hbox{$\boldsymbol{-}$}}$\cr\hidewidth$\boldsymbol{\uparrow}$\hidewidth\cr${\raise-.19ex\hbox{$\boldsymbol{-}$}}$}}}
+\newcommand{\pmrsume}[2]{#1 \mathrel{\rotatebox[origin=c]{90}{$\pmRsum$}} #2} %161.01
+\newcommand{\pmRsume}{\rotatebox[origin=c]{90}{$\pmRsum$} }
+\newcommand{\pmrsumb}[2]{#1 \mathrel{\rotatebox[origin=c]{270}{$\pmRsum$}} #2} %161.02
+\newcommand{\pmRsumb}{\rotatebox[origin=c]{270}{$\pmRsum$}}
+\newcommand{\pmrsumr}[1]{\Sigma\textbf{`}#1} %162.01
+\newcommand{\pmRsumr}{\Sigma}
+\newcommand{\pmrsumrex}[1]{\mathrel{\text{Rel}^{#1}\text{excl}}} %163.01
+\newcommand{\pmsmorsmorb}[2]{#1 \mathrel{\overline{\text{smor}}\,\overline{\text{smor}}} #2} %164.01
+\newcommand{\pmSmorsmorb}{\overline{\text{smor}}\,\overline{\text{smor}}}
+\newcommand{\pmsmorsmor}[2]{#1 \mathrel{\pmSmor\,\pmSmor} #2} %164.02
+\newcommand{\pmSmorsmor}{\pmSmor\,\pmSmor}
+\newcommand{\pmrprod}[2]{#1 \times #2} %166.01
+
+%First differences and the multiplication and exponentiation of relations
+%On the relation of first differences among the sub-classes of a given class
+\newcommand{\pmrfdcl}[3]{#2 \mathrel{#1_{\text{cl}}} #3} %170.01
+\newcommand{\pmRfdcl}[1]{#1_{\text{cl}}}
+\newcommand{\pmrfdlc}[3]{#2 \mathrel{#1_{\text{lc}}} #3} %170.02
+\newcommand{\pmRfdlc}[1]{#1_{\text{lc}}}
+\newcommand{\pmrfddf}[3]{#2 \mathrel{#1_{\text{df}}} #3} %171.01
+\newcommand{\pmRfddf}[1]{#1_{\text{df}}}
+\newcommand{\pmrfdfd}[3]{#2 \mathrel{#1_{\text{fd}}} #3} %171.02
+\newcommand{\pmRfdfd}[1]{#1_{\text{fd}}}
+\newcommand{\pmrfprod}[1]{\Pi\textbf{`}#1} %172.01
+\newcommand{\pmRfprod}[1]{\text{Prod}\textbf{`}#1} %173.01
+\newcommand{\pmrarrel}[1]{\mathrel{\text{Rel}^{#1}\text{arithm}}} %174.01
+\newcommand{\pmrexp}{\mathrel{\text{exp}}} %176.01
+\newcommand{\pmRexp}[2]{{#1}^{#2}} %176.02
+\newcommand{\pmrnsum}[2]{{#1} + {#2}} %180.01
+\newcommand{\pmRnsum}{+}
+\newcommand{\pmrndsum}[2]{{#1} \mathrel{\pmcirc{+}} {#2}} %180.02
+\newcommand{\pmRndsum}{\pmcirc{+}}
+\newcommand{\pmrnsumru}[2]{#1 \mathrel{\pmcirc{\pmRsumb}} #2} %181.01
+\newcommand{\pmRnsumru}{\pmcirc{\pmRsumb}}
+\newcommand{\pmrnsumur}[2]{#1 \mathrel{\pmcirc{\pmRsume}} #2} %181.011
+\newcommand{\pmRnsumur}{\pmcirc{\pmRsume}}
+\newcommand{\pmrn}[1]{\pmcirc{#1}} %181.02
+\newcommand{\pmrsep}[1]{\ooalign{${\raise1.5ex\hbox{\rotatebox[origin=c]{180}{\scalebox{1.4}[1.4]{$\pmbreve{\phantom{.}}$}}}}$\cr\hidewidth$#1$\hidewidth}} %182.01
+\newcommand{\pmrnsumf}[1]{\Sigma\pmNr\textbf{`}#1} %183.01
+\newcommand{\pmrnprod}[2]{#1 \mathrel{\pmcirc{\times}} #2} %184.01
+\newcommand{\pmRnprod}{\pmcirc{\times}}
+\newcommand{\pmrnprodf}[1]{\Pi\pmNr\textbf{`}#1} %185.01
+\newcommand{\pmrnexp}[3]{#2 \mathrel{\pmArexp_{#1}} #3} %186.01
+\newcommand{\pmRnexp}[1]{\pmArexp_{#1}}
+
+%Series
+%General theory of series
+\newcommand{\pmtrans}{\text{trans}} %201.01
+\newcommand{\pmconnex}{\text{connex}} %202.01
+\newcommand{\pmser}{\text{Ser}} %204.01
+\newcommand{\pmseq}[3]{#1 \mathrel{\text{seq}_{#1}} #2} %206.01
+\newcommand{\pmSeq}[1]{\text{seq}_{#1}}
+\newcommand{\pmprec}[3]{#1 \mathrel{\text{prec}_{#1}} #2} %206.02
+\newcommand{\pmPrec}[1]{\text{prec}_{#1}}
+\newcommand{\pmlt}[1]{\text{lt}_{#1}} %207.01
+\newcommand{\pmtl}[1]{\text{tl}_{#1}} %207.01
+\newcommand{\pmlimax}[2]{\text{limax}_{#1}\textbf{`}#2} %207.03
+\newcommand{\pmLimax}[1]{\text{limax}_{#1}}
+\newcommand{\pmlimin}[2]{\text{limin}_{#1}\textbf{`}#2} %207.04
+\newcommand{\pmLimin}[1]{\text{limin}_{#1}}
+\newcommand{\pmcr}[1]{\text{cr}\textbf{`}{#1}}
+\newcommand{\pmCr}{\text{cr}}
+\newcommand{\pmcror}[1]{\text{cror}\textbf{`}{#1}} %208.01
+\newcommand{\pmCror}{\text{cror}}
+
+%On sections, segments, stretches, and derivatives
+\newcommand{\pmsect}[1]{\text{sect}\textbf{`}{#1}} %211.01
+\newcommand{\pmSect}{\text{sect}}
+\newcommand{\pmseg}[1]{\boldsymbol{\varsigma}\textbf{`}{#1}} %212.01
+\newcommand{\pmSeg}{\boldsymbol{\varsigma}}
+\newcommand{\pmsym}[1]{\text{sym}\textbf{`}{#1}} %212.02
+\newcommand{\pmSym}{\text{sym}}
+\newcommand{\pmsectr}[1]{{#1}_{\pmSeg}} %213.01
+\newcommand{\pmded}{\mathrel{\text{Ded}}} %214.01
+\newcommand{\pmsded}{\mathrel{\text{semi}\;\text{Ded}}} %214.02
+\newcommand{\pmstr}[1]{\text{str}\textbf{`}{#1}} %215.01
+\newcommand{\pmStr}{\text{str}}
+\newcommand{\pmder}[2]{\delta_{#1}\textbf{`}#2} %216.01
+\newcommand{\pmDer}[1]{\delta_{#1}}
+\newcommand{\pmdern}[3]{\delta_{#1}^{#2}\textbf{`}#3}
+\newcommand{\pmden}[1]{\text{dense}\textbf{`}{#1}} %216.02
+\newcommand{\pmDen}{\text{dense}}
+\newcommand{\pmclsd}[1]{\text{closed}\textbf{`}{#1}} %216.03
+\newcommand{\pmClsd}{\text{closed}}
+\newcommand{\pmperf}[1]{\text{perf}\textbf{`}{#1}} %216.04
+\newcommand{\pmPerf}{\text{perf}}
+\newcommand{\pmders}[1]{\rotatebox[origin=c]{180}{$\Delta$}\textbf{`}#1} %216.05
+\newcommand{\pmDers}{\rotatebox[origin=c]{180}{$\Delta$}}
+
+%On convergence, and the limits of functions
+\newcommand{\pmconv}[3]{#1\bar{#2}_{\text{cn}}#3} %230.01
+\newcommand{\pmConv}[1]{{#1}_{\text{cn}}} %230.02
+\newcommand{\pmconvg}[3]{#1\bar{#2}_{\text{cng}}#3}
+\newcommand{\pmConvg}[1]{{#1}_{\text{cng}}}
+\newcommand{\pmlsc}[3]{#1\bar{#2}_{\text{sc}}#3} %231.01
+\newcommand{\pmosc}[3]{#1\bar{#2}_{\text{os}}#3} %231.02
+\newcommand{\pmlscl}[4]{(#1\bar{#2}#3)_{\text{sc}}\textbf{`}#4} %232.01
+\newcommand{\pmoscl}[4]{(#1\bar{#2}#3)_{\text{os}}\textbf{`}#4} %232.02
+\newcommand{\pmlmx}[4]{(#1\bar{#2}#3)_{\text{lmx}}\textbf{`}#4} %233.01
+\newcommand{\pmLmx}[3]{(#1\bar{#2}#3)_{\text{lmx}}}
+\newcommand{\pmlimf}[4]{#1(#2#3)\textbf{`}#4} %233.02
+\newcommand{\pmLimf}[3]{#1(#2#3)}
+\newcommand{\pmscf}[3]{\text{sc}(#1, #2)\boldsymbol{`}#3} %234.01
+\newcommand{\pmosf}[3]{\text{os}(#1, #2)\boldsymbol{`}#3} %234.02
+\newcommand{\pmctf}[3]{\text{ct}(#1#2)\boldsymbol{`}#3} %234.03
+\newcommand{\pmcontinf}[3]{\text{contin}(#1#2)\boldsymbol{`}#3} %234.04
+\newcommand{\pmcontin}[2]{#1 \mathrel{\text{contin}} #2} %234.05
+\newcommand{\pmContin}{\text{contin}}
+
+%Volume III
+%Well-Ordered Series
+\newcommand{\pmbord}{\text{Bord}} %250.01
+\newcommand{\pmword}{\Omega} %250.02
+\newcommand{\pmordn}{\text{NO}} %251.01
+\newcommand{\pmless}{\mathrel{\text{less}}} %254.01
+\newcommand{\pmLess}{\text{less}}
+\newcommand{\pmpsc}[2]{#1 \mathrel{P_{\text{sm}}} #2} %254.02
+\newcommand{\pmPsc}{P_{\text{sm}}}
+\newcommand{\pmorle}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth$\boldsymbol{\cdot}$}}} %255.01
+\newcommand{\pmorgr}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr$\boldsymbol{\cdot}$\hidewidth}}} %255.02
+\newcommand{\pmnoo}{\text{N}_0\text{O}} %255.03
+\newcommand{\pmorleq}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth$\boldsymbol{\cdot}$\cr\hidewidth${\raise-.75ex\hbox{\rotatebox[origin=c]{155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}\hspace{-.375ex}$}}} %255.04
+\newcommand{\pmorgrq}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr$\boldsymbol{\cdot}$\hidewidth\cr${\hspace{-.4ex}\raise-.75ex\hbox{\rotatebox[origin=c]{-155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}$\hidewidth}}} %255.05
+\newcommand{\pmm}{\emph{M}} %256.01
+\newcommand{\pmn}{\emph{N}} %256.02, 263.02
+\newcommand{\pmtranc}[3]{(#1\pmast#2)\textbf{`}#3} %257.01
+\newcommand{\pmTranc}[2]{(#1\pmast#2)} %257.01
+\newcommand{\pmtrpot}[3]{#1_{#2#3}} %257.02
+\newcommand{\pma}{\emph{A}} %259.01
+\newcommand{\pmaw}{\emph{A}_{\emph{W}}} %259.02
+\newcommand{\pmwa}{\emph{W}_{\emph{A}}} %259.03
+
+%Finite and Infinite Series and Ordinals
+\newcommand{\pmintf}{P_{\text{fn}}} %260.01
+\newcommand{\pmserinf}{\text{Ser infin}} %261.01
+\newcommand{\pmwordinf}{\pmword\text{ infin}} %261.02
+\newcommand{\pmserfin}{\text{Ser fin}} %261.03
+\newcommand{\pmwordfin}{\pmword\text{ fin}} %261.04
+\newcommand{\pmwordind}{\pmword\text{ induct}} %261.04
+\newcommand{\pmordnfin}{\text{NO fin}} %262.01
+\newcommand{\pmordninf}{\text{NO infin}} %262.02
+\newcommand{\pmfinord}[1]{#1_r} %262.03
+\newcommand{\pmom}{\boldsymbol{\omega}} %263.01
+\newcommand{\pmpr}[1]{#1_{\text{pr}}} %264.01
+\newcommand{\pmomn}[1]{\pmom_{#1}} %265.01, 265.03, etc.
+\newcommand{\pmalephn}[1]{\pmaleph_{#1}} %265.02, 265.04, etc.
+
+%Compact series, rational series, and continuous series
+\newcommand{\pmcomp}{\mathrel{\text{comp}}} %270.01
+\newcommand{\pmComp}{\text{Comp}}
+\newcommand{\pmmed}{\mathrel{\text{med}}} %271.01
+\newcommand{\pmMed}{\text{med}}
+\newcommand{\pmsimp}[3]{\mathrel{#1_{#2#3}}} %272.01
+\newcommand{\pmsimps}[3]{{#1}_{#2}\textbf{`}{#3}} %273.02
+\newcommand{\pmSimp}[3]{({#1}{#2})_{#3}} %273.03
+\newcommand{\pmSimps}[2]{{#1}_{#2}} %273.04
+\newcommand{\pmrats}{\eta} %273.01
+\newcommand{\pmsfcls}[1]{#1_\pmrats} %274.01
+\newcommand{\pmsfclsm}[2]{#1_m\textbf{`}#2} %274.02
+\newcommand{\pmsfclsp}[2]{\pmbreve{#1}_P\textbf{`}{#2}} %274.03
+\newcommand{\pmsfclsmp}[1]{M_P\textbf{`}{#1}} %274.04
+\newcommand{\pmcser}{\theta} %275.01
+\newcommand{\pmcsercl}[1]{#1_\pmcser} %276.01
+\newcommand{\pmcsercls}[2]{{#1}_{#2}} %276.04
+\newcommand{\pmCsercls}[2]{{#1}_{\text{tl}}\textbf{`}{#2}} %264.05
+%Skipped some temprary definitions as repetitious
+
+%Quantity
+%Generalization of Number
+\newcommand{\pmu}{\textit{U}} %300.01
+\newcommand{\pmrnum}{\text{Rel num}} %300.02
+\newcommand{\pmrnumid}{\text{Rel num id}} %300.03
+\newcommand{\pmrpwr}[2]{#1^#2} %301.03
+\newcommand{\pmPrm}{\text{Prm}} %302.01
+\newcommand{\pmrprm}[4]{(#1,#2)\mathbin{\pmPrm_\tau}(#3,#4)} %302.02
+\newcommand{\pmprm}[4]{(#1,#2)\mathbin{\pmPrm}(#3,#4)} %302.03
+\newcommand{\pmhcf}[2]{\text{hcf}(#1,#2)} %302.04
+\newcommand{\pmHcf}{\text{hcf}}
+\newcommand{\pmlcm}[2]{\text{lcm}(#1,#2)} %302.05
+\newcommand{\pmLcm}{\text{lcm}}
+\newcommand{\pmrat}[2]{#1 \rotatebox[origin=c]{10}{$\boldsymbol{/}$} #2} %303.01
+\newcommand{\pmqn}[1]{#1_q} %303.02
+\newcommand{\pmqnil}{\infty_q} %303.03
+\newcommand{\pmRat}{\text{Rat}} %303.04
+\newcommand{\pmRatdef}{\text{Rat def}} %303.05
+\newcommand{\pmqnle}[2]{#1 \mathrel{\boldsymbol{<}_r} #2} %304.01
+\newcommand{\pmQnle}{\boldsymbol{<}_r}
+\newcommand{\pmqnLe}{H} %304.02
+\newcommand{\pmqnlez}{H'} %304.03
+\newcommand{\pmprodsr}[2]{#1 \times_s #2} %305.01
+\newcommand{\pmProdsr}{\times_s}
+\newcommand{\pmsumsr}[2]{#1 +_s #2} %306.01
+\newcommand{\pmSumsr}{+_s}
+\newcommand{\pmratn}{\text{Rat}_n} %307.01
+\newcommand{\pmratg}{\text{Rat}_g} %307.011
+\newcommand{\pmratnle}[2]{#1 \mathrel{\boldsymbol{<}_n} #2} %307.02
+\newcommand{\pmRatnle}{\boldsymbol{<}_n}
+\newcommand{\pmatngr}[2]{#1 \mathrel{\boldsymbol{>}_n} #2} %307.021
+\newcommand{\pmRatngr}{\boldsymbol{>}_n}
+\newcommand{\pmratgle}[2]{#1 \mathrel{\boldsymbol{<}_g} #2} %307.03
+\newcommand{\pmRatgle}{\boldsymbol{<}_g}
+\newcommand{\pmratggr}[2]{#1 \mathrel{\boldsymbol{>}_g} #2} %307.031
+\newcommand{\pmRatggr}{\boldsymbol{>}_g}
+\newcommand{\pmratnLe}{H_n} %307.04
+\newcommand{\pmratgLe}{H_g} %307.05
+\newcommand{\pmratssub}[2]{#1 \boldsymbol{-}_s #2} %308.01
+\newcommand{\pmsumgr}[2]{#1 +_g #2} %308.02
+\newcommand{\pmprodgr}[2]{#1 \times_g #2} %309.01
+\newcommand{\pmrenp}{\Theta} %310.01
+\newcommand{\pmrenpz}{\Theta'} %310.011
+\newcommand{\pmrenn}{\Theta_n} %310.02
+\newcommand{\pmrennz}{\Theta_n'} %310.021
+\newcommand{\pmreng}{\Theta_g} %310.03
+\newcommand{\pmconc}[1]{\text{concord}(#1)} %311.01
+\newcommand{\pmConc}{\text{concord}}
+\newcommand{\pmrensumc}[2]{#1 +_p #2} %311.02
+\newcommand{\pmrensub}[2]{#1 -_p #2} %312.01
+\newcommand{\pmrensuma}[2]{#1 +_a #2} %312.02
+\newcommand{\pmrenproda}[2]{#1 \times_a #2} %313.01
+\newcommand{\pmrenrsum}[2]{#1 +_r #2} %314.01
+\newcommand{\pmrenrprod}[2]{#1 \times_r #2} %314.02
+\newcommand{\Male}{{\usefont{U}{mvs}{m}{n}\symbol{124}}} %from the Marvosym package
+\newcommand{\pmrenr}{\mathop{\text{\Male}}} %314.03
+\newcommand{\pmrenrssum}[2]{#1 +_\sigma #2} %314.04
+\newcommand{\pmrenrsprod}[2]{#1 \times_\sigma #2} %313.05
+
+%Vector Families
+\newcommand{\pmcorr}[1]{\text{cr}\textbf{`}#1} %330.01
+\newcommand{\pmabel}{\text{Abel}} %330.02
+\newcommand{\pmvfm}[1]{\text{fm}\textbf{`}#1} %330.03
+\newcommand{\pmVfm}{\text{fm}}
+\newcommand{\pmvfmcl}{\textit{FM}} %330.04
+\newcommand{\pmvffb}[1]{#1_\iota} %330.05
+\newcommand{\pmconx}[1]{\text{conx}\textbf{`}#1} %331.01
+\newcommand{\pmconxfm}{\textit{FM}\text{ conx}} %331.02
+\newcommand{\pmfrep}[2]{\text{rep}_#1\textbf{`}#2} %332.01
+\newcommand{\pmfopen}[1]{#1_\partial} %333.01
+\newcommand{\pmfopennid}[1]{#1_{\iota\partial}} %333.011
+\newcommand{\pmfmap}{\textit{FM}\text{ ap}} %333.02
+\newcommand{\pmfmapconx}{\textit{FM}\text{ ap conx}} %333.03
+\newcommand{\pmtrsp}[1]{\text{trs}\textbf{`}#1} %334.01
+\newcommand{\pmfmtrs}{\textit{FM}\text{ trs}} %334.02
+\newcommand{\pmfmconnex}{\textit{FM}\text{ connex}} %334.03
+\newcommand{\pmfmsr}{\textit{FM}\text{ sr}} %334.02
+\newcommand{\pmfmasym}{\textit{FM}\text{ asym}} %334.05
+\newcommand{\pminit}[1]{\text{init}\textbf{`}#1} %335.01
+\newcommand{\pmfminit}{\textit{FM}\text{ init}} %335.02
+\newcommand{\pmvr}[1]{\textit{V}_#1} %336.01
+\newcommand{\pmvrnid}[1]{\textit{U}_#1} %336.011
+\newcommand{\pmarvs}[1]{A_{#1}} %336.02
+
+%Measurement
+\newcommand{\pmfmsubm}{\textit{FM}\text{ subm}} %351.01
+\newcommand{\pmvrm}[2]{#1_#2} %352.01
+\newcommand{\pmvrmg}[2]{#1_{#2\iota}} %352.02
+\newcommand{\pmfmrt}{\textit{FM}\text{ rt}} %353.01
+\newcommand{\pmfmcx}{\textit{FM}\text{ cx}} %353.02
+\newcommand{\pmfmrtcx}{\textit{FM}\text{ rt cx}} %353.03
+\newcommand{\pmfmg}[1]{#1_g} %354.01
+\newcommand{\pmrtnet}[2]{\text{cx}_#1\textbf{`}#2} %354.02
+\newcommand{\pmfmgrp}{\textit{FM}\text{ grp}} %354.03
+\newcommand{\pmrems}[2]{#1_#2} %356.01
+
+%Cyclic Families
+\newcommand{\pmfmcycl}{\textit{FM}\text{ cycl}} %370.01
+\newcommand{\pmcycl}[2]{#1_#2} %370.02
+\newcommand{\pmcycli}[2]{#1_#2} %370.03
+\newcommand{\pmvser}[2]{#1_#2} %371.01
+\newcommand{\pmintsecvser}[2]{#1_#2} %372.01
+\newcommand{\pmprime}{\text{Prime}} %373.01
+\newcommand{\pmsfmid}[3]{#1_{#2#3}} %373.02
+\newcommand{\pmsmltid}[2]{(#1, #2)} %373.03
+\newcommand{\pmprrt}[3]{(#1 \rotatebox[origin=c]{10}{$\boldsymbol{/}$} #2)_{#3}} %375.01 \ No newline at end of file
diff --git a/macros/latex/contrib/principia/principia.tex b/macros/latex/contrib/principia/principia.tex
index 86d5ce3a22..8c5eb4e7bf 100644
--- a/macros/latex/contrib/principia/principia.tex
+++ b/macros/latex/contrib/principia/principia.tex
@@ -1,13 +1,13 @@
\documentclass[12pt]{article}
\NeedsTeXFormat{LaTeX2e}
-\ProvidesPackage{principia}[2021/04/19 principia package version 1.3] %This is the principia package is for representing notations in Whitehead and Russell's ``Principia Mathematica" close to their appearance in the original.
+\ProvidesPackage{principia}[2023/03/13 principia package version 2.0] %This is the principia package is for representing notations in Whitehead and Russell's ``Principia Mathematica" close to their appearance in the original.
%Version 1.0 (superseded by Version 1.1): Covers typesetting of notation through Volume I. 2020/10/24
%Version 1.1 (superseded by Version 1.2) minor updates: fixed the spacing of scope dots around parentheses; fixed spacing of theorem sign; fixed spacing around primitive proposition and definition signs. 2020/10/25
%Licensed under LaTeX Project Public License 1.3c.
-%Version 1.2 (superseded by Version 1.3) (minor updates): boldfaced (`thickened') the truth-functional connectives, existential quantifier, set and relation symbols; added numerous commands for typesetting brackets and substitutions into theorems. 2021/02/25
-%Version 1.3 (minor update): removes package dependency on marvosym; updates Section A and Section B notations. 2021/04/19
+%Version 1.2 (superseded by Version 2.0) (minor updates): boldfaced (`thickened') the truth-functional connectives, existential quantifier, set and relation symbols; added numerous commands for typesetting brackets and substitutions into theorems. 2021/02/25
+%Version 2.0 (major update): extends the package to cover typesetting of all notations in Volume II; removes package dependency on marvosym. 2023/03/13
%Licensed under LaTeX Project Public License 1.3c.
-%Copyright Landon D. C. Elkind, 2021. (https://landondcelkind.com/contact/).
+%Copyright Landon D. C. Elkind, 2022. (https://landonelkind.com/contact/).
\usepackage{fullpage}
\usepackage[T1]{fontenc}
@@ -24,6 +24,26 @@
%Mathematical logic
%The theory of deduction
%Meta-logical symbols
+\newcommand{\ie}{\textit{i}.\textit{e}.\ }
+\newcommand{\Ie}{\textit{I}.\textit{e}.\ }
+\newcommand{\eg}{\textit{e}.\textit{g}.\ }
+\newcommand{\Eg}{\textit{E}.\textit{g}.\ }
+\newcommand{\pmsch}[1]{\pmast#1} %Starred chapter
+\newcommand{\pmschs}[2]{\pmast#1\text{---}\pmast#2} %Starred chapter
+\newcommand{\pmsns}[3]{\pmast#1\pmcdot#2\text{---}\pmcdot#3}%Starred number
+\newcommand{\pmpsn}[2]{(\pmast#1\pmcdot#2)}
+\newcommand{\pmpsnn}[3]{(\pmast#1\pmcdot#2\pmcdot#3)}
+\newcommand{\pmsn}[2]{\pmast#1\pmcdot#2}
+\newcommand{\pmnsn}[1]{\text{#1}}
+\newcommand{\pmsnn}[3]{\pmast#1\pmcdot#2\pmcdot#3}
+\newcommand{\pmsnnn}[4]{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4}
+\newcommand{\pmsnnnn}[5]{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5}
+\newcommand{\pmsnnnnn}[6]{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5\pmcdot#6}
+\newcommand{\pmsnb}[2]{\boldsymbol{\pmast#1\pmcdot#2}} %Starred number boldface
+\newcommand{\pmsnnb}[3]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3}}
+\newcommand{\pmsnnnb}[4]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4}}
+\newcommand{\pmsnnnnb}[5]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5}}
+\newcommand{\pmsnnnnnb}[6]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5\pmcdot#6}}
\newcommand{\pmfd}{\begin{center} \rule{5cm}{.5pt} \end{center}} %Dividing line between introductory remarks in a starred number and the formal deductions.
\newcommand{\pmdem}{\textit{Dem}.} %This notation begins a proof.
\newcommand{\pmdemi}{\indent \pmdem} %This idents the notation that begins a proof.
@@ -38,7 +58,7 @@
\newcommand{\pmSub}[3]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array} \bigg \rbrack} %This is the substitution command.
\newcommand{\pmSubb}[5]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array} \bigg \rbrack} %This is the substitution command.
\newcommand{\pmSubbb}[7]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array} \bigg \rbrack} %This is the substitution command.
-\newcommand{\pmSubbbb}[9]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array} \bigg \rbrack} %This is the substitution command.
+\newcommand{\pmSubbbb}[9]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c c} #2, & #4, & #6, & #8 \\ \hline #3, & #5, & #7, & #9 \end{array} \bigg \rbrack} %This is the substitution command.
\newcommand{\pmsUb}[2]{\small \begin{array}{c} #1 \\ \hline #2 \end{array}} %This is the substitution command.
\newcommand{\pmsUbb}[4]{\small \begin{array}{c c} #1, & #3 \\ \hline #2, & #4 \end{array}} %This is the substitution command.
\newcommand{\pmsUbbb}[6]{\small \begin{array}{c c c} #1, & #3, & #5 \\ \hline #2, & #4, & #6 \end{array}} %This is the substitution command.
@@ -46,12 +66,13 @@
\newcommand{\pmSUb}[3]{\normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array}} %This is the substitution command.
\newcommand{\pmSUbb}[5]{\normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array}} %This is the substitution command.
\newcommand{\pmSUbbb}[7]{\normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array}} %This is the substitution command.
-\newcommand{\pmSUbbbb}[9]{\normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}} %This is the substitution command.
+\newcommand{\pmSUbbbb}[9]{\normalsize #1 \text{ } \small \begin{array}{c c c c} #2, & #4, & #6, & #8 \\ \hline #3, & #5, & #7, & #9 \end{array}} %This is the substitution command.
\newcommand{\pmthm}{\mathpunct{\text{\scalebox{.5}[1]{$\boldsymbol\vdash$}}}} %This is the theorem sign.
\newcommand{\pmast}{\text{\resizebox{!}{.75\height}{\ding{107}}}} %This is the sign introducing a theorem number.
\newcommand{\pmcdot}{\text{\raisebox{.05cm}{$\boldsymbol\cdot$}}} %This is a sign introducing a theorem sub-number.
\newcommand{\pmiddf}{\mathbin{=}}
\newcommand{\pmdf}{\quad \text{Df}}
+\newcommand{\pmDf}{\text{Df}}
\newcommand{\pmpp}{\quad \text{Pp}}
%Square dots for scope, defined for up to six dots
@@ -74,6 +95,7 @@
\newcommand{\pmandddddd}{\pmandd\hspace{.1em}\pmandd\hspace{.1em}\pmandd}
\newcommand{\pmprod}{\mathbin{\ooalign{$\boldsymbol{\wedge}\mkern.5mu$\hidewidth\cr$\boldsymbol{\wedge}$\cr\hidewidth$\mkern.5mu\boldsymbol{\wedge}$}}} %Not in Principia, but added here as a dual of its symbol for disjunction.
\newcommand{\pmiff}{\mathbin{\ooalign{$\boldsymbol{\equiv}\mkern.5mu$\hidewidth\cr$\boldsymbol{\equiv}$\cr\hidewidth$\mkern.5mu\boldsymbol{\equiv}$}}} %4.01
+\newcommand{\pminc}{\mathbin{|}} %8.01
%The theory of apparent variables
\newcommand{\pmall}[1]{(#1)}
@@ -81,24 +103,574 @@
\newcommand{\pmSome}{\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}}
%Additional defined logic signs
-\newcommand{\pmhat}[1]{\mathbf{\hat{\text{$#1$}}}}
-\newcommand{\pmbreve}[1]{\mathbf{\breve{\text{$#1$}}}}
-\newcommand{\pmcirc}[1]{\mathbf{\dot{\text{$#1$}}}}
+\newcommand{\pmhat}[1]{\boldsymbol{\hat{\text{$#1$}}}}
+\newcommand{\pmbreve}[1]{\boldsymbol{\breve{\text{$#1$}}}}
+\newcommand{\pmcirc}[1]{\boldsymbol{\dot{\text{$#1$}}}}
\newcommand{\pmpf}[2]{#1#2} %for propositional functions of one variable
\newcommand{\pmpff}[3]{#1(#2, #3)} %for propositional functions of two variables
\newcommand{\pmpfff}[4]{#1(#2, #3, #4)} %for propositional functions of three variables
+\newcommand{\pmpffff}[5]{#1(#2, #3, #4, #5)} %for propositional functions of four variables (including ellipses)
+\newcommand{\pmppf}[2]{#1\pmshr#2} %for propositional predicative functions of one variable
+\newcommand{\pmppff}[3]{#1\pmshr(#2, #3)} %for propositional predicative functions of two variables
\newcommand{\pmshr}{\textbf{!}} %*12.1 and *12.11, used for predicative propositional functions
\newcommand{\pmpred}[2]{#1\pmshr#2} %for predicates (``predicative functions'') of one variable
\newcommand{\pmpredd}[3]{#1\pmshr(#2, #3)} %for predicates (``predicative functions'') of two variables
\newcommand{\pmpreddd}[4]{#1\pmshr(#2, #3, #4)} %for predicates (``predicative functions'') of three variables
+\newcommand{\pmpredddd}[5]{#1\pmshr(#2, #3, #4, #5)} %for predicates (``predicative functions'') of four variables
+\newcommand{\pmpreddddd}[6]{#1\pmshr(#2, #3, #4, #5, #6)} %for predicates (``predicative functions'') of five variables
+\newcommand{\pmpredddddd}[7]{#1\pmshr(#2, #3, #4, #5, #6, #7)} %for predicates (``predicative functions'') of six variables
+\newcommand{\pmid}{\mathbin{=}}
\newcommand{\pmnid}{\mathrel{\ooalign{$=$\cr\hidewidth\footnotesize\rotatebox[origin=c]{210}{\textbf{/}}\hidewidth\cr}}} %*13.02
-\newcommand{\pmiota}{\ooalign{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}\cr\hidewidth\raisebox{.0125em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.025em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.0375em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.05em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}}} %the rotated Greek iota used in definite descriptions
+\newcommand{\pmiota}{\ooalign{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}\cr\hidewidth\raisebox{.0125em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}\cr\hidewidth\raisebox{.025em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}\cr\hidewidth\raisebox{.0375em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}\cr\hidewidth\raisebox{.05em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}}} %the rotated Greek iota used in definite descriptions
\newcommand{\pmdsc}[1]{(\pmiota#1)} %*14.01
+\newcommand{\pmthe}[2]{(\pmiota#1)(#2 #1)} %*14.01
+\newcommand{\pmtheb}[2]{[(\pmiota#1)(#2 #1)]} %*14.01
\newcommand{\pmDsc}{\pmiota}
\newcommand{\pmexists}{\textbf{E}\hspace{.1em}\pmshr} %*14.02
-\title{\texttt{principia.sty}\\ A \LaTeXe \space Package for Typesetting Whitehead and Russell's \textit{Principia Mathematica} (Version 1.3)}
-\author{Landon D. C. Elkind \texttt{elkind@ualberta.ca}}
+%Classes and relations
+%Class signs
+\newcommand{\pmcls}[2]{\pmhat{#1}(#2)} %20.01
+\newcommand{\pmcin}{\mathop{\boldsymbol{\epsilon}}} %20.02
+\newcommand{\pmCls}{\text{Cls}} %20.03
+\newcommand{\pmClsn}[1]{\text{Cls}^{#1}}
+\newcommand{\pmcinn}{\pmnot\pmcin} %20.06
+\newcommand{\pmcinc}{\mathop{\ooalign{$\boldsymbol{\subset}$\cr\hidewidth$\hspace{.1em}\boldsymbol{\subset}$\cr\hidewidth$\hspace{.15em}\boldsymbol{\subset}$\cr\hidewidth$\hspace{.2em}\boldsymbol{\subset}$}}} %22.01
+\newcommand{\pmccap}{\mathop{\ooalign{\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.1em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.2em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.3em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.4em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.5em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.6em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}}}} %22.02
+\newcommand{\pmccup}{\mathop{\ooalign{\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.1em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.2em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.3em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.4em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.5em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.6em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}}}} %22.03
+\newcommand{\pmccmp}[1]{\boldsymbol{-}#1} %22.04
+\newcommand{\pmcmin}[2]{#1\boldsymbol{-}#2} %22.05
+\newcommand{\pmcuni}{\text{\rotatebox[origin=c]{180}{$\Lambda$}}} %24.01
+\newcommand{\pmcnull}{\Lambda} %24.02
+\newcommand{\pmcexists}{\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}\hspace{-.1em}\mathop{\pmshr}} %24.03
+
+%Relation signs
+\newcommand{\pmrel}[3]{\pmhat{#1}\pmhat{#2}#3} %21.01
+\newcommand{\pmrele}[5]{#1\{\pmhat{#2}\pmhat{#3}#4(#2, #3)\}#5} %21.02
+\newcommand{\pmrelep}[3]{#1\{#2\}#3} %21.08, 21.081, 21.082, etc.
+\newcommand{\pmrcmp}[1]{\ooalign{$\hidewidth\raisebox{.25em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccmp}$}#1} %23.04
+\newcommand{\pmrmin}[2]{#1\mathrel{\ooalign{$\hidewidth\raisebox{.25em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccmp}$}}#2} %23.05
+\newcommand{\pmruni}{\pmcirc{\text{\rotatebox[origin=c]{180}{$\Lambda$}}}} %25.01
+\newcommand{\pmrnull}{\pmcirc{\Lambda}} %25.02
+\newcommand{\pmrexists}{\pmcirc{\mathop{\text{\raisebox{.5em}{\rotatebox{180}{E}}}}}\mathop{\pmshr}} %25.03
+\newcommand{\pmrinc}{\mathrel{\ooalign{$\hidewidth\boldsymbol{\cdot}\hidewidth$\cr$\boldsymbol{\pmcinc}$}}} %23.01
+\newcommand{\pmrcap}{\mathrel{\ooalign{$\hidewidth\raisebox{.3em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccap}$}}} %23.02
+\newcommand{\pmrcup}{\mathrel{\ooalign{$\hidewidth\raisebox{.1em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccup}$}}} %23.03
+
+%Logic of Relations
+\newcommand{\pmdscf}[2]{#1\textbf{`}#2} %30.01
+\newcommand{\pmcnv}[1]{\text{Cnv}\textbf{`}#1} %31.01
+\newcommand{\pmCnv}{\text{Cnv}}
+\newcommand{\pmcrel}[1]{\pmbreve{#1}} %31.02
+\newcommand{\pmrrf}[2]{\overset{\boldsymbol{\rightarrow}}{#1\textbf{`}}#2} %32.01
+\newcommand{\pmRrf}[1]{\overset{\boldsymbol{\rightarrow}}{#1}}
+\newcommand{\pmrrl}[2]{\overset{\boldsymbol{\leftarrow}}{#1\textbf{`}}#2} %32.02
+\newcommand{\pmRrl}[1]{\overset{\boldsymbol{\leftarrow}}{#1}}
+\newcommand{\pmsg}[1]{\text{sg}\textbf{`}#1} %32.03
+\newcommand{\pmSg}{\text{sg}}
+\newcommand{\pmgs}[1]{\text{gs}\textbf{`}#1} %32.04
+\newcommand{\pmGs}{\text{gs}}
+\newcommand{\pmdm}[1]{\text{D}\textbf{`}#1} %33.01
+\newcommand{\pmDm}{\text{D}}
+\newcommand{\pmcdm}[1]{\text{\rotatebox[origin=c]{180}{D}}\textbf{`}#1} %33.02
+\newcommand{\pmCdm}{\text{\rotatebox[origin=c]{180}{D}}}
+\newcommand{\pmcmp}[1]{C\textbf{`}#1} %33.03
+\newcommand{\pmCmp}{C}
+\newcommand{\pmfld}[1]{F\textbf{`}#1} %33.04
+\newcommand{\pmFld}{F}
+\newcommand{\pmrprd}[2]{{#1}\mathop{|}{#2}} %34.01
+\newcommand{\pmRprd}{\mathop{|}}
+\newcommand{\pmrprdn}[2]{#1^{#2}} %34.02, 34.03, etc.
+\newcommand{\pmrld}[2]{#1 \boldsymbol{\upharpoonleft} #2} %35.01
+\newcommand{\pmrlcd}[2]{#1 \boldsymbol{\upharpoonright} #2} %35.02
+\newcommand{\pmrlf}[3]{#1 \boldsymbol{\upharpoonleft} #2 \boldsymbol{\upharpoonright} #3} %35.03
+\newcommand{\pmrl}[2]{#1 \boldsymbol{\uparrow} #2} %35.04
+\newcommand{\pmrlF}[2]{#1 \mathbin{\ooalign{$\upharpoonright$\cr\hidewidth\rotatebox[origin=c]{180}{\text{$\upharpoonleft$}}\hidewidth\cr}} #2} %36.01
+\newcommand{\pmdscff}[2]{#1\textbf{`}\textbf{`}#2} %37.01
+\newcommand{\pmdscfr}[2]{#1_{\pmcin}\textbf{`}#2} %37.02
+\newcommand{\pmdscfR}[1]{#1_{\pmcin}}
+\newcommand{\pmdscfcr}[2]{\pmbreve{#1}_{\pmcin}\textbf{`}#2} %37.03
+\newcommand{\pmdscfcR}[1]{\pmbreve{#1}_{\pmcin}}
+\newcommand{\pmdscfff}[2]{#1\textbf{`}\textbf{`}\textbf{`}#2} %37.04
+\newcommand{\pmdscfe}[2]{\mathop{\text{E}}\mathop{\pmshr\pmshr}\pmdscff{#1}{#2}} %37.05
+\newcommand{\Female}{{\usefont{U}{mvs}{m}{n}\symbol{126}}} %from the Marvosym package
+\newcommand{\pmop}{\mathop{\text{\Female}}} %38.01, 38.02
+\newcommand{\pmopc}[2]{#1 \mathop{\underset{\textbf{''}}{\text{\Female}}} #2} %38.03
+
+%Products and sums of classes of classes or relations
+\newcommand{\pmccsum}[1]{p\textbf{`}#1} %40.01
+\newcommand{\pmccprd}[1]{s\textbf{`}#1} %40.02
+\newcommand{\pmcrsum}[1]{\pmcirc{p}\textbf{`}#1} %41.01
+\newcommand{\pmcrprd}[1]{\pmcirc{s}\textbf{`}#1} %41.02
+\newcommand{\pmrprdd}[2]{{#1}\mathop{||}{#2}} %43.01
+\newcommand{\pmRprdd}{\mathop{||}}
+
+%Prolegomena to Cardinal Arithmetic
+%Unit Classes and Couples
+%Identity and Diversity
+\newcommand{\pmrid}{I} %50.01
+\newcommand{\pmrdiv}{J} %50.02
+\newcommand{\pmcunit}[1]{\iota\textbf{`}#1} %51.01
+\newcommand{\pmcUnit}{\iota}
+\newcommand{\pmcunits}[1]{\pmbreve{\iota}\textbf{`}#1} %52.01
+
+%Cardinal numbers
+\newcommand{\pmcn}[1]{#1} %52.01, 54.01, 54.02, etc.
+
+%Ordinal numbers
+\newcommand{\pmoc}[2]{#1 \boldsymbol{\downarrow} #2} %55.01, 55.02, etc.
+\newcommand{\pmdn}[1]{\pmcirc{#1}} %56.01
+\newcommand{\pmorn}[1]{#1_r} %56.02, 56.03, etc.
+
+%Sub-classes, Sub-relations, and Relative Types
+%Sub-classes
+\newcommand{\pmscl}[1]{\text{Cl}\textbf{`}#1} %60.01
+\newcommand{\pmsCl}{\text{Cl}}
+\newcommand{\pmscle}[1]{\text{Cl ex}\textbf{`}#1} %60.02
+\newcommand{\pmsCle}{\text{Cl ex}}
+\newcommand{\pmscls}[1]{\text{Cls}\textbf{`}#1} %60.03
+\newcommand{\pmsrl}[1]{\text{Rl}\textbf{`}#1} %61.01
+\newcommand{\pmsRl}{\text{Rl}}
+\newcommand{\pmsrle}[1]{\text{Rl ex}\textbf{`}#1} %61.02
+\newcommand{\pmsRle}{\text{Rl ex}}
+\newcommand{\pmsrel}[1]{\text{Rel}\textbf{`}#1} %61.03
+\newcommand{\pmRel}{\text{Rel}}
+\newcommand{\pmReln}[1]{\text{Rel}^{#1}} %61.04
+\newcommand{\pmrin}{\mathop{\boldsymbol{\epsilon}}} %62.01
+
+%Relative type symbols
+\newcommand{\pmrt}[1]{t\textbf{`}#1} %63.01
+\newcommand{\pmrti}[2]{t^{#1}\textbf{`}#2} %63.011
+\newcommand{\pmrtc}[2]{t_{#1}\textbf{`}#2} %63.02, 63.03, etc.
+\newcommand{\pmrtri}[2]{t^{#1}\textbf{`}#2} %63.04
+\newcommand{\pmrtrc}[2]{t_{#1}\textbf{`}#2} %64.02, 64.021, 64.022, etc.
+\newcommand{\pmrtrci}[3]{t_{#1}^{\text{ }#2}\textbf{`}#3} %64.03, 64.031, etc.
+\newcommand{\pmrtric}[3]{{}^{#1}t_{#2}\textbf{`}#3} %64.04, 64.041, etc.
+\newcommand{\pmrtdi}[2]{#1_{#2}} %65.01
+\newcommand{\pmrtdc}[2]{#1(#2)} %65.02
+\newcommand{\pmrtdri}[2]{#1_{#2}} %65.03
+\newcommand{\pmrtdrc}[2]{#1(#2)} %65.04
+
+%One-many, Many-one, and One-one relations
+%Similarity relation signs
+\newcommand{\pmrdc}[2]{#1\boldsymbol{\to}#2} %70.01
+\newcommand{\pmsmbar}{\mathrel{\overline{\text{sm}}}} %73.01
+\newcommand{\pmsm}{\mathrel{\text{sm}}} %73.02
+\newcommand{\pmSM}{\text{sm}}
+\newcommand{\pmsmarr}{\overrightarrow{{\pmsm}}}
+\newcommand{\pmonemany}{1\boldsymbol{\to}\pmCls}
+\newcommand{\pmmanyone}{\pmCls\boldsymbol{\to}1}
+\newcommand{\pmoneone}{1\boldsymbol{\to}1}
+
+%Selections
+\newcommand{\pmselp}[1]{P_{\small\Delta}\boldsymbol{`}#1} %80.01
+\newcommand{\pmSelp}{P_{\Delta}}
+\newcommand{\pmsele}[1]{\pmcin_{\small\Delta}\boldsymbol{`}#1}
+\newcommand{\pmSele}{\pmcin_{\Delta}}
+\newcommand{\pmself}[1]{F_{\small\Delta}\boldsymbol{`}#1}
+\newcommand{\pmSelf}{F_{\Delta}}
+\newcommand{\pmexc}{\text{Cls}^2 \mathop{\text{excl}}} %84.01
+\newcommand{\pmexcc}[1]{\text{Cl} \mathop{\text{excl}}\textbf{`}#1} %84.02
+\newcommand{\pmex}{\text{Cls excl}}
+\newcommand{\pmexcn}{\text{Cls} \mathop{\text{ex}^2} \mathop{\text{excl}}} %84.03
+\newcommand{\pmselc}[2]{#1 \mathrel{\ooalign{\rotatebox[origin=c]{270}{$\boldsymbol{\mapsto}$}}} #2}
+\newcommand{\pmmultr}{\mathop{\text{Rel}} \mathop{\text{Mult}}} %88.01
+\newcommand{\pmmultc}{\mathop{\text{Cls}^2} \mathop{\text{Mult}}} %88.02
+\newcommand{\pmmultax}{\mathop{\text{Mult}} \mathop{\text{ax}}} %88.03
+
+%Inductive relations
+\newcommand{\pmanc}[1]{#1_\pmast} %90.01
+\newcommand{\pmancc}[1]{\pmcrel{#1}_\pmast} %90.02
+\newcommand{\pmrst}[1]{#1_\text{st}} %91.01
+\newcommand{\pmrts}[1]{#1_\text{ts}} %91.02
+\newcommand{\pmpot}[1]{\text{Pot}\boldsymbol{`}#1} %91.03
+\newcommand{\pmpotid}[1]{\text{Potid}\boldsymbol{`}#1} %91.04
+\newcommand{\pmpo}[1]{#1_\text{po}} %91.05
+\newcommand{\pmB}{B} %93.01
+\newcommand{\pmmin}[1]{\text{min}_{#1}} %93.02
+\newcommand{\pmMin}{\text{min}}
+\newcommand{\pmmax}[1]{\text{max}_{#1}} %93.021
+\newcommand{\pmMax}{\text{max}}
+\newcommand{\pmgen}[1]{\text{gen}\boldsymbol{`}#1} %93.03
+\newcommand{\pmGen}{\text{gen}}
+\newcommand{\pmefr}[2]{#1\pmast#2} %95.05
+\newcommand{\pmipr}[2]{I_{#1}\textbf{`}#2} %96.01
+\newcommand{\pmjpr}[2]{J_{#1}\textbf{`}#2} %96.02
+\newcommand{\pmfr}[2]{\overset{\boldsymbol{\leftrightarrow}}{#1}\textbf{`}#2} %97.01
+
+%Volume II
+%Cardinal arithmetic
+%Definition and Logical Properties of Cardinal Numbers
+\newcommand{\pmnc}[1]{\text{Nc}\textbf{`}#1} %100.01
+\newcommand{\pmNc}{\text{Nc}}
+\newcommand{\pmNC}{\text{NC}} %100.02
+\newcommand{\pmNCat}[2]{\text{NC}^{#1}({#2})} %102.01
+\newcommand{\pmnoc}[1]{\text{N}_0\text{c}\textbf{`}#1} %103.01
+\newcommand{\pmNoc}{\text{N}_0\text{c}}
+\newcommand{\pmNoC}{\text{N}_0\text{C}} %103.02
+\newcommand{\pmnca}[2]{\text{N}^{#1}\text{c}\textbf{`}#2} %104.01, 104.011, etc.
+\newcommand{\pmNca}[1]{\text{N}^{#1}\text{C}} %104.02, 104.021, etc.
+\newcommand{\pmch}[2]{#1^{(#2)}} %104.03, 104.031, etc.
+\newcommand{\pmncd}[2]{\text{N}_{#1}\text{c}\textbf{`}#2} %105.01
+\newcommand{\pmNcd}[1]{\text{N}_{#1}\text{C}} %105.02, 105.021, etc.
+\newcommand{\pmcl}[2]{#1_{(#2)}} %105.03, 105.031, etc.
+\newcommand{\pmncll}[3]{\text{N}_{#1#2}\text{c}\textbf{`}#3} %106.01, 106.012, etc.
+\newcommand{\pmnchh}[3]{\text{N}^{#1#2}\text{c}\textbf{`}#3} %106.011
+\newcommand{\pmncaa}[3]{\text{N}_{#1}{}^{#2}\text{c}\textbf{`}#3} %106.02
+\newcommand{\pmncdd}[3]{{}^{#1}\text{N}_{#2}\text{c}\textbf{`}#3} %106.021
+\newcommand{\pmNCll}[2]{\text{N}_{#1#2}\text{C}} %106.03
+\newcommand{\pmNChh}[2]{\text{N}^{#1#2}\text{C}}
+\newcommand{\pmcll}[3]{#1_{(#2#3)}} %106.04
+\newcommand{\pmchh}[3]{#1^{(#2#3)}} %106.041
+\newcommand{\pmncr}[1]{\text{N}_{00}\text{c}\textbf{`}#1} %106.01
+
+%Addition, Multiplication, Exponentiation
+\newcommand{\pmarsumc}{\mathrel{+}} %110.01
+\newcommand{\pmarsumnc}{\mathrel{{+}_{\text{c}}}} %110.02
+\newcommand{\pmsmsmb}{\mathrel{\overline{\text{sm}}\;\overline{\text{sm}}}} %111.01
+\newcommand{\pmcrp}[2]{\text{Crp}(#1)\textbf{`}#2} %111.02
+\newcommand{\pmsmsm}{\mathrel{\text{sm}\;\text{sm}}} %111.03
+\newcommand{\pmarsumcc}[1]{\Sigma\textbf{`}#1} %112.01
+\newcommand{\pmarsumcnc}[1]{\Sigma\pmNc\textbf{`}#1} %112.02
+\newcommand{\pmarprodc}{\times} %113.02
+\newcommand{\pmarprodnc}{\times_\text{c}} %113.03
+\newcommand{\pmarprodcnc}[1]{\Pi\pmNc\textbf{`}#1} %114.01
+\newcommand{\pmarprodcc}[1]{\text{Prod}\textbf{`}#1} %115.01
+\newcommand{\pmarcls}{\pmClsn{3}\text{arithm}} %115.02
+\newcommand{\pmarexp}[2]{#1 \mathrel{\text{exp}} #2} %116.01
+\newcommand{\pmArexp}{\text{exp}}
+\newcommand{\pmarncexp}[2]{#1^{#2}} %116.02
+\newcommand{\pmarg}{\mathrel{\boldsymbol{>}}} %117.01
+\newcommand{\pmarl}{\mathrel{\boldsymbol{<}}} %117.04
+\newcommand{\pmargeq}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr${\hspace{-.4ex}\raise-.75ex\hbox{\rotatebox[origin=c]{-155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}$}}} %117.05
+\newcommand{\pmarleq}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth${\raise-.75ex\hbox{\rotatebox[origin=c]{155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}\hspace{-.375ex}$}}} %117.06
+
+%Finite and infinite
+\newcommand{\pmarsubt}[2]{#1 \mathrel{{-}_\text{c}} #2} %119.01
+\newcommand{\pmArsubt}{{-}_\text{c}}
+\newcommand{\pmNCinduct}{\text{NC}\,\text{induct}} %120.01
+\newcommand{\pmncinduct}[1]{\text{N}_#1\text{C}\,\text{induct}} %120.011
+\newcommand{\pmClsinduct}{\text{Cls}\,\text{induct}} %120.02
+\newcommand{\pmclsinduct}[1]{\text{Cls}_{#1}\,\text{induct}} %120.021
+\newcommand{\pmInfinax}{\text{Infin}\,\text{ax}} %120.03
+\newcommand{\pminfinax}[1]{\text{Infin}\,\text{ax}(#1)} %120.04
+\newcommand{\pmspec}[1]{\text{spec}\textbf{`}#1} %120.43
+\newcommand{\pmintoo}[2]{P(#1\mathbin{\boldsymbol{-}}#2)} %121.01
+\newcommand{\pmintoc}[2]{P({#1}\mathbin{\scalebox{1.2}[.7]{$\boldsymbol{\dashv}$}}{#2})} %121.011
+\newcommand{\pmintco}[2]{P({#1}\mathbin{\scalebox{1.2}[.7]{$\boldsymbol{\vdash}$}}{#2})} %121.012
+\newcommand{\pmintcc}[2]{P({#1} \mathbin{\ooalign{$\scalebox{1.2}[.7]{$\boldsymbol{\dashv}$}$\hidewidth\cr$\scalebox{1.2}[.7]{$\boldsymbol{\vdash}$}$}} {#2})} %121.013
+\newcommand{\pmintnc}[1]{P_{#1}} %121.02
+\newcommand{\pmfinid}[1]{\text{finid}\textbf{`}#1} %121.03
+\newcommand{\pmfin}[1]{\text{fin}\textbf{`}#1} %121.031
+\newcommand{\pmintt}[2]{#1_{#2}} %121.04
+\newcommand{\pmprog}{\text{Prog}} %122.01
+\newcommand{\pmaleph}{\boldsymbol{\aleph}} %123.01
+\newcommand{\pmsucc}{\text{N}} %123.02
+\newcommand{\pmclsrefl}{\text{Cls}\;\text{refl}} %124.01
+\newcommand{\pmncrefl}{\text{NC}\;\text{refl}} %124.02
+\newcommand{\pmncmult}{\text{NC}\;\text{mult}} %124.03
+\newcommand{\pmncind}{\text{NC}\;\text{ind}} %126.01
+\newcommand{\pmnocind}[1]{\text{N}_0\text{Cinduct}\textbf{`}#1}
+\newcommand{\pmNocind}{\text{N}_0\text{Cinduct}}
+
+%Relation-arithmetic
+%Ordinal similarity and relation-numbers
+\newcommand{\pmrnsm}[2]{{#1}{\raise.4ex\hbox{\textbf{\large;}}}{#2}} %150.01
+\newcommand{\pmrnsmd}[2]{#1 \mathop{\boldsymbol{\dagger}} #2} %150.02
+\newcommand{\pmrnsmdf}[1]{#1\boldsymbol{\dagger}}
+\newcommand{\pmopsc}[2]{#1 \mathrel{\ooalign{${\raise-.7ex\hbox{$\pmdot$}}$\hidewidth\cr$\text{\Female}$\hidewidth\cr${\raise-.8ex\hbox{\hspace{.15cm}\textbf{,}}}$}} #2} %150.03
+\newcommand{\pmsmorb}[2]{#1 \mathrel{\overline{\text{smor}}} #2} %151.01
+\newcommand{\pmSmorb}{\overline{\text{smor}}} %151.01
+\newcommand{\pmsmor}[2]{#1 \mathrel{\text{smor}} #2} %151.02
+\newcommand{\pmSmor}{\text{smor}}
+\newcommand{\pmnr}[1]{\text{Nr}\textbf{`}#1} %152.01
+\newcommand{\pmNr}{\text{Nr}}
+\newcommand{\pmNR}{\text{NR}} %152.02
+\newcommand{\pmsrrn}[1]{{#1}_{s}} %153.01
+\newcommand{\pmNRat}[2]{\text{NR}^{#1}({#2})} %154.01
+\newcommand{\pmnor}[1]{\text{N}_0\text{r}\textbf{`}#1} %155.01
+\newcommand{\pmNor}{\text{N}_0\text{r}}
+\newcommand{\pmNoR}{\text{N}_0\text{R}} %155.02
+
+%Addition of Relations, and the Product of Two Relations
+\newcommand{\pmrsum}[2]{#1\mathrel{\ooalign{${\raise-.21ex\hbox{$\boldsymbol{-}$}}$\cr\hidewidth$\boldsymbol{\uparrow}$\hidewidth\cr${\raise-.19ex\hbox{$\boldsymbol{-}$}}$}} #2} %160.01
+\newcommand{\pmRsum}{\mathrel{\ooalign{${\raise-.21ex\hbox{$\boldsymbol{-}$}}$\cr\hidewidth$\boldsymbol{\uparrow}$\hidewidth\cr${\raise-.19ex\hbox{$\boldsymbol{-}$}}$}}}
+\newcommand{\pmrsume}[2]{#1 \mathrel{\rotatebox[origin=c]{90}{$\pmRsum$}} #2} %161.01
+\newcommand{\pmRsume}{\rotatebox[origin=c]{90}{$\pmRsum$} }
+\newcommand{\pmrsumb}[2]{#1 \mathrel{\rotatebox[origin=c]{270}{$\pmRsum$}} #2} %161.02
+\newcommand{\pmRsumb}{\rotatebox[origin=c]{270}{$\pmRsum$}}
+\newcommand{\pmrsumr}[1]{\Sigma\textbf{`}#1} %162.01
+\newcommand{\pmRsumr}{\Sigma}
+\newcommand{\pmrsumrex}[1]{\mathrel{\text{Rel}^{#1}\text{excl}}} %163.01
+\newcommand{\pmsmorsmorb}[2]{#1 \mathrel{\overline{\text{smor}}\,\overline{\text{smor}}} #2} %164.01
+\newcommand{\pmSmorsmorb}{\overline{\text{smor}}\,\overline{\text{smor}}}
+\newcommand{\pmsmorsmor}[2]{#1 \mathrel{\pmSmor\,\pmSmor} #2} %164.02
+\newcommand{\pmSmorsmor}{\pmSmor\,\pmSmor}
+\newcommand{\pmrprod}[2]{#1 \times #2} %166.01
+
+%First differences and the multiplication and exponentiation of relations
+%On the relation of first differences among the sub-classes of a given class
+\newcommand{\pmrfdcl}[3]{#2 \mathrel{#1_{\text{cl}}} #3} %170.01
+\newcommand{\pmRfdcl}[1]{#1_{\text{cl}}}
+\newcommand{\pmrfdlc}[3]{#2 \mathrel{#1_{\text{lc}}} #3} %170.02
+\newcommand{\pmRfdlc}[1]{#1_{\text{lc}}}
+\newcommand{\pmrfddf}[3]{#2 \mathrel{#1_{\text{df}}} #3} %171.01
+\newcommand{\pmRfddf}[1]{#1_{\text{df}}}
+\newcommand{\pmrfdfd}[3]{#2 \mathrel{#1_{\text{fd}}} #3} %171.02
+\newcommand{\pmRfdfd}[1]{#1_{\text{fd}}}
+\newcommand{\pmrfprod}[1]{\Pi\textbf{`}#1} %172.01
+\newcommand{\pmRfprod}[1]{\text{Prod}\textbf{`}#1} %173.01
+\newcommand{\pmrarrel}[1]{\mathrel{\text{Rel}^{#1}\text{arithm}}} %174.01
+\newcommand{\pmrexp}{\mathrel{\text{exp}}} %176.01
+\newcommand{\pmRexp}[2]{{#1}^{#2}} %176.02
+\newcommand{\pmrnsum}[2]{{#1} + {#2}} %180.01
+\newcommand{\pmRnsum}{+}
+\newcommand{\pmrndsum}[2]{{#1} \mathrel{\pmcirc{+}} {#2}} %180.02
+\newcommand{\pmRndsum}{\pmcirc{+}}
+\newcommand{\pmrnsumru}[2]{#1 \mathrel{\pmcirc{\pmRsumb}} #2} %181.01
+\newcommand{\pmRnsumru}{\pmcirc{\pmRsumb}}
+\newcommand{\pmrnsumur}[2]{#1 \mathrel{\pmcirc{\pmRsume}} #2} %181.011
+\newcommand{\pmRnsumur}{\pmcirc{\pmRsume}}
+\newcommand{\pmrn}[1]{\pmcirc{#1}} %181.02
+\newcommand{\pmrsep}[1]{\ooalign{${\raise1.5ex\hbox{\rotatebox[origin=c]{180}{\scalebox{1.4}[1.4]{$\pmbreve{\phantom{.}}$}}}}$\cr\hidewidth$#1$\hidewidth}} %182.01
+\newcommand{\pmrnsumf}[1]{\Sigma\pmNr\textbf{`}#1} %183.01
+\newcommand{\pmrnprod}[2]{#1 \mathrel{\pmcirc{\times}} #2} %184.01
+\newcommand{\pmRnprod}{\pmcirc{\times}}
+\newcommand{\pmrnprodf}[1]{\Pi\pmNr\textbf{`}#1} %185.01
+\newcommand{\pmrnexp}[3]{#2 \mathrel{\pmArexp_{#1}} #3} %186.01
+\newcommand{\pmRnexp}[1]{\pmArexp_{#1}}
+
+%Series
+%General theory of series
+\newcommand{\pmtrans}{\text{trans}} %201.01
+\newcommand{\pmconnex}{\text{connex}} %202.01
+\newcommand{\pmser}{\text{Ser}} %204.01
+\newcommand{\pmseq}[3]{#1 \mathrel{\text{seq}_{#1}} #2} %206.01
+\newcommand{\pmSeq}[1]{\text{seq}_{#1}}
+\newcommand{\pmprec}[3]{#1 \mathrel{\text{prec}_{#1}} #2} %206.02
+\newcommand{\pmPrec}[1]{\text{prec}_{#1}}
+\newcommand{\pmlt}[1]{\text{lt}_{#1}} %207.01
+\newcommand{\pmtl}[1]{\text{tl}_{#1}} %207.01
+\newcommand{\pmlimax}[2]{\text{limax}_{#1}\textbf{`}#2} %207.03
+\newcommand{\pmLimax}[1]{\text{limax}_{#1}}
+\newcommand{\pmlimin}[2]{\text{limin}_{#1}\textbf{`}#2} %207.04
+\newcommand{\pmLimin}[1]{\text{limin}_{#1}}
+\newcommand{\pmcr}[1]{\text{cr}\textbf{`}{#1}}
+\newcommand{\pmCr}{\text{cr}}
+\newcommand{\pmcror}[1]{\text{cror}\textbf{`}{#1}} %208.01
+\newcommand{\pmCror}{\text{cror}}
+
+%On sections, segments, stretches, and derivatives
+\newcommand{\pmsect}[1]{\text{sect}\textbf{`}{#1}} %211.01
+\newcommand{\pmSect}{\text{sect}}
+\newcommand{\pmseg}[1]{\boldsymbol{\varsigma}\textbf{`}{#1}} %212.01
+\newcommand{\pmSeg}{\boldsymbol{\varsigma}}
+\newcommand{\pmsym}[1]{\text{sym}\textbf{`}{#1}} %212.02
+\newcommand{\pmSym}{\text{sym}}
+\newcommand{\pmsectr}[1]{{#1}_{\pmSeg}} %213.01
+\newcommand{\pmded}{\mathrel{\text{Ded}}} %214.01
+\newcommand{\pmsded}{\mathrel{\text{semi}\;\text{Ded}}} %214.02
+\newcommand{\pmstr}[1]{\text{str}\textbf{`}{#1}} %215.01
+\newcommand{\pmStr}{\text{str}}
+\newcommand{\pmder}[2]{\delta_{#1}\textbf{`}#2} %216.01
+\newcommand{\pmDer}[1]{\delta_{#1}}
+\newcommand{\pmdern}[3]{\delta_{#1}^{#2}\textbf{`}#3}
+\newcommand{\pmden}[1]{\text{dense}\textbf{`}{#1}} %216.02
+\newcommand{\pmDen}{\text{dense}}
+\newcommand{\pmclsd}[1]{\text{closed}\textbf{`}{#1}} %216.03
+\newcommand{\pmClsd}{\text{closed}}
+\newcommand{\pmperf}[1]{\text{perf}\textbf{`}{#1}} %216.04
+\newcommand{\pmPerf}{\text{perf}}
+\newcommand{\pmders}[1]{\rotatebox[origin=c]{180}{$\Delta$}\textbf{`}#1} %216.05
+\newcommand{\pmDers}{\rotatebox[origin=c]{180}{$\Delta$}}
+
+%On convergence, and the limits of functions
+\newcommand{\pmconv}[3]{#1\bar{#2}_{\text{cn}}#3} %230.01
+\newcommand{\pmConv}[1]{{#1}_{\text{cn}}} %230.02
+\newcommand{\pmconvg}[3]{#1\bar{#2}_{\text{cng}}#3}
+\newcommand{\pmConvg}[1]{{#1}_{\text{cng}}}
+\newcommand{\pmlsc}[3]{#1\bar{#2}_{\text{sc}}#3} %231.01
+\newcommand{\pmosc}[3]{#1\bar{#2}_{\text{os}}#3} %231.02
+\newcommand{\pmlscl}[4]{(#1\bar{#2}#3)_{\text{sc}}\textbf{`}#4} %232.01
+\newcommand{\pmoscl}[4]{(#1\bar{#2}#3)_{\text{os}}\textbf{`}#4} %232.02
+\newcommand{\pmlmx}[4]{(#1\bar{#2}#3)_{\text{lmx}}\textbf{`}#4} %233.01
+\newcommand{\pmLmx}[3]{(#1\bar{#2}#3)_{\text{lmx}}}
+\newcommand{\pmlimf}[4]{#1(#2#3)\textbf{`}#4} %233.02
+\newcommand{\pmLimf}[3]{#1(#2#3)}
+\newcommand{\pmscf}[3]{\text{sc}(#1, #2)\boldsymbol{`}#3} %234.01
+\newcommand{\pmosf}[3]{\text{os}(#1, #2)\boldsymbol{`}#3} %234.02
+\newcommand{\pmctf}[3]{\text{ct}(#1#2)\boldsymbol{`}#3} %234.03
+\newcommand{\pmcontinf}[3]{\text{contin}(#1#2)\boldsymbol{`}#3} %234.04
+\newcommand{\pmcontin}[2]{#1 \mathrel{\text{contin}} #2} %234.05
+\newcommand{\pmContin}{\text{contin}}
+
+%Volume III
+%Well-Ordered Series
+\newcommand{\pmbord}{\text{Bord}} %250.01
+\newcommand{\pmword}{\Omega} %250.02
+\newcommand{\pmordn}{\text{NO}} %251.01
+\newcommand{\pmless}{\mathrel{\text{less}}} %254.01
+\newcommand{\pmLess}{\text{less}}
+\newcommand{\pmpsc}[2]{#1 \mathrel{P_{\text{sm}}} #2} %254.02
+\newcommand{\pmPsc}{P_{\text{sm}}}
+\newcommand{\pmorle}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth$\boldsymbol{\cdot}$}}} %255.01
+\newcommand{\pmorgr}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr$\boldsymbol{\cdot}$\hidewidth}}} %255.02
+\newcommand{\pmnoo}{\text{N}_0\text{O}} %255.03
+\newcommand{\pmorleq}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth$\boldsymbol{\cdot}$\cr\hidewidth${\raise-.75ex\hbox{\rotatebox[origin=c]{155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}\hspace{-.375ex}$}}} %255.04
+\newcommand{\pmorgrq}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr$\boldsymbol{\cdot}$\hidewidth\cr${\hspace{-.4ex}\raise-.75ex\hbox{\rotatebox[origin=c]{-155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}$\hidewidth}}} %255.05
+\newcommand{\pmm}{\emph{M}} %256.01
+\newcommand{\pmn}{\emph{N}} %256.02, 263.02
+\newcommand{\pmtranc}[3]{(#1\pmast#2)\textbf{`}#3} %257.01
+\newcommand{\pmTranc}[2]{(#1\pmast#2)} %257.01
+\newcommand{\pmtrpot}[3]{#1_{#2#3}} %257.02
+\newcommand{\pma}{\emph{A}} %259.01
+\newcommand{\pmaw}{\emph{A}_{\emph{W}}} %259.02
+\newcommand{\pmwa}{\emph{W}_{\emph{A}}} %259.03
+
+%Finite and Infinite Series and Ordinals
+\newcommand{\pmintf}{P_{\text{fn}}} %260.01
+\newcommand{\pmserinf}{\text{Ser infin}} %261.01
+\newcommand{\pmwordinf}{\pmword\text{ infin}} %261.02
+\newcommand{\pmserfin}{\text{Ser fin}} %261.03
+\newcommand{\pmwordfin}{\pmword\text{ fin}} %261.04
+\newcommand{\pmwordind}{\pmword\text{ induct}} %261.04
+\newcommand{\pmordnfin}{\text{NO fin}} %262.01
+\newcommand{\pmordninf}{\text{NO infin}} %262.02
+\newcommand{\pmfinord}[1]{#1_r} %262.03
+\newcommand{\pmom}{\boldsymbol{\omega}} %263.01
+\newcommand{\pmpr}[1]{#1_{\text{pr}}} %264.01
+\newcommand{\pmomn}[1]{\pmom_{#1}} %265.01, 265.03, etc.
+\newcommand{\pmalephn}[1]{\pmaleph_{#1}} %265.02, 265.04, etc.
+
+%Compact series, rational series, and continuous series
+\newcommand{\pmcomp}{\mathrel{\text{comp}}} %270.01
+\newcommand{\pmComp}{\text{Comp}}
+\newcommand{\pmmed}{\mathrel{\text{med}}} %271.01
+\newcommand{\pmMed}{\text{med}}
+\newcommand{\pmsimp}[3]{\mathrel{#1_{#2#3}}} %272.01
+\newcommand{\pmsimps}[3]{{#1}_{#2}\textbf{`}{#3}} %273.02
+\newcommand{\pmSimp}[3]{({#1}{#2})_{#3}} %273.03
+\newcommand{\pmSimps}[2]{{#1}_{#2}} %273.04
+\newcommand{\pmrats}{\eta} %273.01
+\newcommand{\pmsfcls}[1]{#1_\pmrats} %274.01
+\newcommand{\pmsfclsm}[2]{#1_m\textbf{`}#2} %274.02
+\newcommand{\pmsfclsp}[2]{\pmbreve{#1}_P\textbf{`}{#2}} %274.03
+\newcommand{\pmsfclsmp}[1]{M_P\textbf{`}{#1}} %274.04
+\newcommand{\pmcser}{\theta} %275.01
+\newcommand{\pmcsercl}[1]{#1_\pmcser} %276.01
+\newcommand{\pmcsercls}[2]{{#1}_{#2}} %276.04
+\newcommand{\pmCsercls}[2]{{#1}_{\text{tl}}\textbf{`}{#2}} %264.05
+%Skipped some temprary definitions as repetitious
+
+%Quantity
+%Generalization of Number
+\newcommand{\pmu}{\textit{U}} %300.01
+\newcommand{\pmrnum}{\text{Rel num}} %300.02
+\newcommand{\pmrnumid}{\text{Rel num id}} %300.03
+\newcommand{\pmrpwr}[2]{#1^#2} %301.03
+\newcommand{\pmPrm}{\text{Prm}} %302.01
+\newcommand{\pmrprm}[4]{(#1,#2)\mathbin{\pmPrm_\tau}(#3,#4)} %302.02
+\newcommand{\pmprm}[4]{(#1,#2)\mathbin{\pmPrm}(#3,#4)} %302.03
+\newcommand{\pmhcf}[2]{\text{hcf}(#1,#2)} %302.04
+\newcommand{\pmHcf}{\text{hcf}}
+\newcommand{\pmlcm}[2]{\text{lcm}(#1,#2)} %302.05
+\newcommand{\pmLcm}{\text{lcm}}
+\newcommand{\pmrat}[2]{#1 \rotatebox[origin=c]{10}{$\boldsymbol{/}$} #2} %303.01
+\newcommand{\pmqn}[1]{#1_q} %303.02
+\newcommand{\pmqnil}{\infty_q} %303.03
+\newcommand{\pmRat}{\text{Rat}} %303.04
+\newcommand{\pmRatdef}{\text{Rat def}} %303.05
+\newcommand{\pmqnle}[2]{#1 \mathrel{\boldsymbol{<}_r} #2} %304.01
+\newcommand{\pmQnle}{\boldsymbol{<}_r}
+\newcommand{\pmqnLe}{H} %304.02
+\newcommand{\pmqnlez}{H'} %304.03
+\newcommand{\pmprodsr}[2]{#1 \times_s #2} %305.01
+\newcommand{\pmProdsr}{\times_s}
+\newcommand{\pmsumsr}[2]{#1 +_s #2} %306.01
+\newcommand{\pmSumsr}{+_s}
+\newcommand{\pmratn}{\text{Rat}_n} %307.01
+\newcommand{\pmratg}{\text{Rat}_g} %307.011
+\newcommand{\pmratnle}[2]{#1 \mathrel{\boldsymbol{<}_n} #2} %307.02
+\newcommand{\pmRatnle}{\boldsymbol{<}_n}
+\newcommand{\pmatngr}[2]{#1 \mathrel{\boldsymbol{>}_n} #2} %307.021
+\newcommand{\pmRatngr}{\boldsymbol{>}_n}
+\newcommand{\pmratgle}[2]{#1 \mathrel{\boldsymbol{<}_g} #2} %307.03
+\newcommand{\pmRatgle}{\boldsymbol{<}_g}
+\newcommand{\pmratggr}[2]{#1 \mathrel{\boldsymbol{>}_g} #2} %307.031
+\newcommand{\pmRatggr}{\boldsymbol{>}_g}
+\newcommand{\pmratnLe}{H_n} %307.04
+\newcommand{\pmratgLe}{H_g} %307.05
+\newcommand{\pmratssub}[2]{#1 \boldsymbol{-}_s #2} %308.01
+\newcommand{\pmsumgr}[2]{#1 +_g #2} %308.02
+\newcommand{\pmprodgr}[2]{#1 \times_g #2} %309.01
+\newcommand{\pmrenp}{\Theta} %310.01
+\newcommand{\pmrenpz}{\Theta'} %310.011
+\newcommand{\pmrenn}{\Theta_n} %310.02
+\newcommand{\pmrennz}{\Theta_n'} %310.021
+\newcommand{\pmreng}{\Theta_g} %310.03
+\newcommand{\pmconc}[1]{\text{concord}(#1)} %311.01
+\newcommand{\pmConc}{\text{concord}}
+\newcommand{\pmrensumc}[2]{#1 +_p #2} %311.02
+\newcommand{\pmrensub}[2]{#1 -_p #2} %312.01
+\newcommand{\pmrensuma}[2]{#1 +_a #2} %312.02
+\newcommand{\pmrenproda}[2]{#1 \times_a #2} %313.01
+\newcommand{\pmrenrsum}[2]{#1 +_r #2} %314.01
+\newcommand{\pmrenrprod}[2]{#1 \times_r #2} %314.02
+\newcommand{\Male}{{\usefont{U}{mvs}{m}{n}\symbol{124}}} %from the Marvosym package
+\newcommand{\pmrenr}{\mathop{\text{\Male}}} %314.03
+\newcommand{\pmrenrssum}[2]{#1 +_\sigma #2} %314.04
+\newcommand{\pmrenrsprod}[2]{#1 \times_\sigma #2} %313.05
+
+%Vector Families
+\newcommand{\pmcorr}[1]{\text{cr}\textbf{`}#1} %330.01
+\newcommand{\pmabel}{\text{Abel}} %330.02
+\newcommand{\pmvfm}[1]{\text{fm}\textbf{`}#1} %330.03
+\newcommand{\pmVfm}{\text{fm}}
+\newcommand{\pmvfmcl}{\textit{FM}} %330.04
+\newcommand{\pmvffb}[1]{#1_\iota} %330.05
+\newcommand{\pmconx}[1]{\text{conx}\textbf{`}#1} %331.01
+\newcommand{\pmconxfm}{\textit{FM}\text{ conx}} %331.02
+\newcommand{\pmfrep}[2]{\text{rep}_#1\textbf{`}#2} %332.01
+\newcommand{\pmfopen}[1]{#1_\partial} %333.01
+\newcommand{\pmfopennid}[1]{#1_{\iota\partial}} %333.011
+\newcommand{\pmfmap}{\textit{FM}\text{ ap}} %333.02
+\newcommand{\pmfmapconx}{\textit{FM}\text{ ap conx}} %333.03
+\newcommand{\pmtrsp}[1]{\text{trs}\textbf{`}#1} %334.01
+\newcommand{\pmfmtrs}{\textit{FM}\text{ trs}} %334.02
+\newcommand{\pmfmconnex}{\textit{FM}\text{ connex}} %334.03
+\newcommand{\pmfmsr}{\textit{FM}\text{ sr}} %334.02
+\newcommand{\pmfmasym}{\textit{FM}\text{ asym}} %334.05
+\newcommand{\pminit}[1]{\text{init}\textbf{`}#1} %335.01
+\newcommand{\pmfminit}{\textit{FM}\text{ init}} %335.02
+\newcommand{\pmvr}[1]{\textit{V}_#1} %336.01
+\newcommand{\pmvrnid}[1]{\textit{U}_#1} %336.011
+\newcommand{\pmarvs}[1]{A_{#1}} %336.02
+
+%Measurement
+\newcommand{\pmfmsubm}{\textit{FM}\text{ subm}} %351.01
+\newcommand{\pmvrm}[2]{#1_#2} %352.01
+\newcommand{\pmvrmg}[2]{#1_{#2\iota}} %352.02
+\newcommand{\pmfmrt}{\textit{FM}\text{ rt}} %353.01
+\newcommand{\pmfmcx}{\textit{FM}\text{ cx}} %353.02
+\newcommand{\pmfmrtcx}{\textit{FM}\text{ rt cx}} %353.03
+\newcommand{\pmfmg}[1]{#1_g} %354.01
+\newcommand{\pmrtnet}[2]{\text{cx}_#1\textbf{`}#2} %354.02
+\newcommand{\pmfmgrp}{\textit{FM}\text{ grp}} %354.03
+\newcommand{\pmrems}[2]{#1_#2} %356.01
+
+%Cyclic Families
+\newcommand{\pmfmcycl}{\textit{FM}\text{ cycl}} %370.01
+\newcommand{\pmcycl}[2]{#1_#2} %370.02
+\newcommand{\pmcycli}[2]{#1_#2} %370.03
+\newcommand{\pmvser}[2]{#1_#2} %371.01
+\newcommand{\pmintsecvser}[2]{#1_#2} %372.01
+\newcommand{\pmprime}{\text{Prime}} %373.01
+\newcommand{\pmsfmid}[3]{#1_{#2#3}} %373.02
+\newcommand{\pmsmltid}[2]{(#1, #2)} %373.03
+\newcommand{\pmprrt}[3]{(#1 \rotatebox[origin=c]{10}{$\boldsymbol{/}$} #2)_{#3}} %375.01
+
+\title{\texttt{principia.sty}\\ A \LaTeXe \space Package for Typesetting Whitehead and Russell's \textit{Principia Mathematica} (Version 2.0)}
+\author{Landon D. C. Elkind \texttt{landon.elkind@wku.edu}}
\date{\today}
\begin{document}
@@ -110,7 +682,7 @@ The \texttt{principia} package is designed for typesetting the Peanese notation
In \textit{Principia Mathematica} some symbols occur with an argument and sometimes that same symbol occurs without an argument. For example, `$\pmsome{x}$' occurs in some formulas, but sometimes `$\pmSome$' occurs in the text when they talk about the symbol itself. \texttt{principia} is designed to accommodate these different occurrences of symbols. When a symbol is to occur without an argument, capitalize the first letter following the `\texttt{$\backslash$pm}' part of the command. E.g. \verb|\pmsome{x}| produces $\pmsome{x}$ and \verb|\pmSome| produces `$\pmSome$'. Note the former command requires an argument and the latter command does not. Not all commands in the \texttt{principia} package admit of such dual use because some symbols in \textit{Principia Mathematica} never occur without an argument or do not take an argument in the usual sense. For example, the propositional connectives do not take an `argument' in the way singular or plural descriptions do.
-Version 1.3 of \texttt{principia} is adequate to typeset all notations throughout Sections A and B of \textit{Principia}'s Volume I and includes some minor fixes. See the package documentation for details.
+Version 2.0 of \texttt{principia} is adequate to typeset all notations throughout Volumes I-III of \textit{Principia} and includes some minor fixes. Below are commands for Volume I.
\texttt{principia}'s dependencies are \texttt{amsmath}, \texttt{amssymb}, \texttt{pifont}, and \texttt{graphicx}. Make sure to load these package by typing \texttt{$\backslash$usepackage\{graphicx\}}, etc., into the document preamble.
@@ -125,7 +697,7 @@ To load \texttt{principia}, type \texttt{$\backslash$usepackage\{principia\}} in
$\pmiddf$ & \verb|\pmiddf| & Identity for definitions (`$=$' differs in spacing). \\
$\pmdf$ & \verb|\pmdf| & Definition. Note the indentation. \\
$\pmdem$ & \verb|\pmdem| & This symbol begins a proof. \\
- $\pmsub{p}{q}$, $\pmsubb{p}{q}{r}{s}$, $\pmsubbb{p}{q}{r}{s}{t}{u}$, ... $\pmSub{\text{Add}}{p}{q}$, ... & \verb|\pmsub{p}{q}|, \verb|\pmsubb{p}{q}{r}{s}|, \verb|\pmsubbb{p}{q}| \par \hfill \verb|{r}{s}{t}{u}|, ... \verb|\pmSub{\text{Add}{p}{q}| & Substitution into theorems. Add `b's to the end of \verb|\pmsub| to increase the number of substitutions (up to four `b's). Each extra `b' adds two arguments. To substitute and specify the theorem as well, capitalize the `s' in \verb|\pmsub|. \\
+ $\pmsub{p}{q}$, $\pmsubb{p}{q}{r}{s}$, $\pmsubbb{p}{q}{r}{s}{t}{u}$, ... $\pmSub{\text{Add}}{p}{q}$, ... & \verb|\pmsub{p}{q}|, \verb|\pmsubb{p}{q}{r}{s}|, \verb|\pmsubbb{p}{q}| \par \hfill \verb|{r}{s}{t}{u}|, ... \verb|\pmSub{\text{Add}}{p}{q}| & Substitution into theorems. Add `b's to the end of \verb|\pmsub| to increase the number of substitutions (up to four `b's). Each extra `b' adds two arguments. To substitute and specify the theorem as well, capitalize the `s' in \verb|\pmsub|. \\
$\pmdot$, $\pmdott$, $\pmdottt$, $\pmdotttt$, $\pmdottttt$, $\pmdotttttt$ & \verb|\pmdot|, \verb|\pmdott|, \verb|\pmdottt|, ... & Add `t's to the end of \verb|\pmdot| to increase the number of dots (up to six `t's). \\
$\pmand$, $\pmandd$, $\pmanddd$, $\pmandddd$, $\pmanddddd$, $\pmandddddd$ & \verb|\pmand|, \verb|\pmandd|, \verb|\pmanddd|, ...& Add `d's to the end of \verb|\pmand| command to increase the number of dots (up to six `d's). \\
$\pmor$ & \verb|\pmor| & Disjunction. \\
@@ -149,7 +721,105 @@ To load \texttt{principia}, type \texttt{$\backslash$usepackage\{principia\}} in
\noindent \begin{tabular}{@{}p{3cm} | p{5cm} | p{8.25cm}}
$=$, $\pmnid$ & \verb|=|, \verb|\pmnid| & Identity and its negation. \\
$\pmdsc{x}$ & \verb|\pmdsc{x}| & Definite description. \\
- $\pmexists$ & \verb|\pmexists| & Existence.
+ $\pmexists$ & \verb|\pmexists| & Existence. \\
+ $\pmcls{z}{\psi z}$ & \verb|\pmcls{z}{\psi z}| & The class of $z$s satisfying $\psi$. \\
+ $\pmcin$ & \verb|\pmcin| & The class membership symbol. \\
+ $\pmClsn{n}$, $\pmCls$ & \verb|\pmClsn{n}|, \verb|\pmCls| & The class of classes of individuals. \\
+ $\pmscl{\alpha}$, $\pmsCl$ & \verb|\pmscl{\alpha}|, \verb|\pmsCl| & The subclasses of a class $\alpha$. \\
+ $\pmsrl{R}$, $\pmsRl$ & \verb|\pmsrl{R}|, \verb|\pmsRl| & The sub-relations of a relation $R$. \\
+ $\pmcuni$ & \verb|\pmcuni| & The universal class. \\
+ $\pmcnull$ & \verb|\pmcnull| & The null class. \\
+ $\pmcexists$ & \verb|\pmcexists| & The existence of a class. \\
+ $\pmccmp{\alpha}$ & \verb|\pmccmp{\alpha}| & This command requires one argument. \\
+ $\pmcmin{\alpha}{\beta}$ & \verb|\pmcmin{\alpha}{\beta}| & This command requires two arguments. \\
+ $\pmccup$ & \verb|\pmccup| & Class union. \\
+ $\pmccap$ & \verb|\pmccap| & Class intersection. \\
+ $\pmcinc$ & \verb|\pmcinc| & Class inclusion. \\
+ $\pmrel{x}{y}{\phi(x,y)}$ & \verb|\pmrel{x}{y}{\phi(x,y)}| & The relation in extension given by $\phi$. \\
+ $\pmrele{a}{x}{y}{R}{b}$ & \verb|\pmrele{a}{x}{y}{R}{b}| & This command requires five arguments. \\
+ $\pmrelep{a}{R}{b}$ & \verb|\pmrelep{a}{R}{b}| & This command requires three arguments. \\
+ $\pmrin$ & \verb|\pmrin| & The relation membership symbol. \\
+ $\pmReln{n}$, $\pmRel$ & \verb|\pmReln{n}|, \verb|\pmRel| & The class of relations ($n$-many `of relations'). \\
+ $\pmruni$ & \verb|\pmruni| & The universal relation. \\
+ $\pmrnull$ & \verb|\pmrnull| & The null relation. \\
+ $\pmrexists$ & \verb|\pmrexists| & This symbol prefixes relations. \\
+ $\pmrcmp{R}$ & \verb|\pmrcmp{\alpha}| & This command requires one argument. \\
+ $\pmrmin{R}{S}$ & \verb|\pmcmin{R}{S}| & This command requires two arguments. \\
+ $\pmrcup$ & \verb|\pmrcup| & Relation union. \\
+ $\pmrcap$ & \verb|\pmrcap| & Relation intersection. \\
+ $\pmrinc$ & \verb|\pmrinc| & Relation inclusion. \\
+ $\pmcrel{R}$ & \verb|\pmcrel{R}| & The converse of a relation. \\
+ $\pmCnv$ & \verb|\pmCnv| & The command for `Cnv'. \\
+ $\pmdscf{R}{x}$ & \verb|\pmdscf{R}{x}| & A singular descriptive function. \\
+ $\pmdscff{R}{\beta}$ & \verb|\pmdscff{R}{\beta}| & A plural descriptive function. \\
+ $\pmdscfff{R}{\kappa}$ & \verb|\pmdscfff{R}{\kappa}| & A plural descriptive function. \\
+ $\pmdscfe{R}{\beta}$ & \verb|\pmdscfe{R}{\beta}| & The existence of a plural descriptive function.
+\end{tabular}
+
+\noindent \begin{tabular}{@{}p{3cm} | p{5cm} | p{8.25cm}}
+ $\pmdscfr{R}{x}$, `$\pmdscfR{R}$'& \verb|\pmdscfr{R}{x}|, \verb|\pmdscfR{R}| & The relation of $\pmdscfr{R}{\beta}$ to $\beta$. \\
+ $\pmdm{R}$, $\pmDm$ & \verb|\pmdm{R}|, \verb|\pmDm| & The domain of a relation $R$. \\
+ $\pmcdm{R}$, $\pmCdm$ & \verb|\pmcdm{R}|, \verb|\pmCdm| & The converse domain of a relation $R$. \\
+ $\pmcmp{R}$, $\pmCmp$ & \verb|\pmcmp{R}|, \verb|\pmCmp| & The campus of a relation $R$. \\
+ $\pmfld{R}$, $\pmFld$ & \verb|\pmfld{R}|, \verb|\pmFld| & The field of a relation $R$. \\
+ $\pmrrf{R}{x}$, $\pmRrf{R}$ & \verb|\pmrrf{R}{x}|, \verb|\pmRrf{R}| & The referents of a given relation. \\
+ $\pmrrl{R}{x}$, $\pmRrl{R}$ & \verb|\pmrrl{R}{x}|, \verb|\pmRrl{R}| & The relata of a given relation. \\
+ $\pmsg{R}$, $\pmSg$ & \verb|\pmsg{R}|, \verb|\pmSg| & \\
+ $\pmgs{R}$, $\pmGs$ & \verb|\pmgs{R}|, \verb|\pmGs| & \\
+ $\pmrprd{R}{S}$, $\pmRprd$ & \verb|\pmrprd{R}{S}|, \verb|\pmrprd| & The relative product of $R$ and $S$. \\
+ $\pmrprdn{R}{n}$ & \verb|\pmrprdn{R}{n}| & The $n$th relative product of $R$. \\
+ $\pmrprdd{R}{S}$, $\pmRprdd$ & \verb|\pmrprdd{R}{S}|, \verb|\pmrprdd| & The double relative product of $R$ and $S$. \\
+ $\pmrlcd{\alpha}{R}$ & \verb|\pmrld{\alpha}{R}| & The limitation of $R$'s domain to $\alpha$. \\
+ $\pmrlcd{R}{\beta}$ & \verb|\pmrld{R}{\beta}| & The limitation of $R$'s converse domain to $\beta$. \\
+ $\pmrlf{\alpha}{R}{\beta}$ & \verb|\pmrlf{\alpha}{R}{\beta}| & The limitation of $R$'s field to $\alpha$ and $\beta$, resp. \\
+ $\pmrlF{P}{\alpha}$ & \verb|\pmrlF{\alpha}{R}{\beta}| & The limitation of $P$'s field to $\alpha$. \\
+ $\pmrl{\alpha}{\beta}$ & \verb|\pmrl{\alpha}{\beta}| & The relation made of all $x$s in $\alpha$ and $y$s in $\beta$. \\
+ $\pmop$ & \verb|\pmop| & The operation symbol. \\
+ $\pmopc{\alpha}{y}$ & \verb|\pmopc{\alpha}{y}| & The relation of $x$s in $\alpha$ taken to $y$ by $\pmop$. \\
+ $\pmccsum{\alpha}$ & \verb|\pmccsum{\alpha}| & The sum of a class of classes. \\
+ $\pmccprd{\alpha}$ & \verb|\pmccprd{\alpha}| & The product of a class of classes. \\
+ $\pmcrsum{\alpha}$ & \verb|\pmcrsum{\alpha}| & The sum of a class of relations. \\
+ $\pmcrprd{\alpha}$ & \verb|\pmcrprd{\alpha}| & The product of a class of relations. \\
+ $\pmrid$, $\pmrdiv$ & \verb|\pmrid|, \verb|\pmrdiv| & The relations of identity and diversity. \\
+ $\pmcunit{x}$, $\pmcUnit$ & \verb|\pmcunit{x}|, \verb|\pmcUnit| & The unit class. \\
+ $\pmcunits{\alpha}$ & \verb|\pmcunits{\alpha}| & The sum of unit classes of $\alpha$'s elements. \\
+ $\pmrn{n}$ & \verb|\pmrn{n}| & The ordinal number $n$. \\
+ $\pmdn{n}$ & \verb|\pmdn{n}| & The class of relations equal to an $n$-tuple. \\
+ $\pmoc{x}{y}$ & \verb|\pmoc{x}{y}| & The ordinal number restricted to $R=(x,y)$. \\
+ $\pmrt{x}$, $\pmrti{n}{x}$ & \verb|\pmrt{x}|, \verb|\pmrti{n}{x}| & The relative type of $x$ ($n$-many `type of's). \\
+ $\pmrtc{n}{\alpha}$ & \verb|\pmrtc{n}{\alpha}| & The relative type of $\alpha$ ($n$-many `type of's). \\
+ $\pmrtri{n}{R}$, $\pmrtrc{n}{R}$ & \verb|\pmrtri{n}{R}|, \verb|\pmrtrc{n}{R}| & The relative type of (with $n$-many `type of's) $R$ from individuals to individuals, or from classes to classes. `$nm$' can replace `$n$'.
+\end{tabular}
+
+\noindent \begin{tabular}{@{}p{3cm} | p{5cm} | p{8.25cm}}
+ $\pmrtric{n}{m}{R}$, $\pmrtrci{n}{m}{R}$ & \verb|\pmrtric{n}{R}|, \verb|\pmrtrci{n}{R}| & The relative type of $R$ from individuals to classes, or from classes to individuals. \\
+ $\pmrtdi{\alpha}{x}$, $\pmrtdri{R}{(x,y)}$ & \verb|\pmrtdi{\alpha}{x}|, \verb|\pmrtdri{R}{(x,y)}| & The result of determining that the members of $\alpha$ ($R$) belong to the relative type of $x$ (in the domain, and of $y$ in the converse domain). \\
+ $\pmrtdc{\alpha}{x}$, $\pmrtdrc{R}{x,y}$ & \verb|\pmrtdc{\alpha}{x}|, \verb|\pmrtdrc{R}{x,y}| & The result of determining that the members of $\alpha$ ($R$) belong to the relative type of $\pmrt{x}$ (in the domain, and of $\pmrt{y}$ in the converse domain). \\
+ $\pmrdc{\alpha}{\beta}$ & \verb|\pmrdc{\alpha}{\beta}| & The class of relations $R$ with domain contained in $\alpha$ and converse domain in $\beta$. \\
+ $\pmoneone$, $\pmonemany$, $\pmmanyone$ & \verb|\pmoneone|, \verb|\pmonemany|, \verb|\pmmanyone| & The class of one-one, or one-many, or many-one, relations. Note \verb|\pmrdc| can be used here. \\
+ $\pmsm$, $\pmsmbar$ & \verb|\pmsm|, \verb|\pmsmbar| & The similarity relation. \\
+ $\pmselp{\kappa}$, $\pmSelp$ & \verb|\pmselp{\kappa}|, \verb|\pmSelp| & The $P$-selections from $\kappa$ \\
+ $\pmsele{\kappa}$, $\pmSele$ & \verb|\pmsele{\kappa}|, \verb|\pmSele| & The $\pmcin$-selections from $\kappa$ \\
+ $\pmself{\kappa}$, $\pmSelf$ & \verb|\pmself{\kappa}|, \verb|\pmSelf| & The $F$-selections from $\kappa$ \\
+ $\pmexc$ & \verb|\pmexc| & The class of pairwise-disjoint classes. \\
+ $\pmexcn$ & \verb|\pmexcn| & The class of pairwise-disjoint non-null classes. \\
+ $\pmexcc{\gamma}$ & \verb|\pmexcc{\gamma}| & A class of mutually exclusive classes in $\gamma$. \\
+ $\pmselc{P}{y}$ & \verb|\pmselc{P}{y}| & The class of couples $(y, \pmdscf{P}{y})$. \\
+ $\pmmultc$ & \verb|\pmmultc| & The class of multipliable classes. \\
+ $\pmmultr$ & \verb|\pmmultr| & The class of multipliable relations. \\
+ $\pmmultax$ & \verb|\pmmultax| & The multiplicative axiom. \\
+ $\pmanc{R}$, $\pmancc{R}$ & \verb|\pmanc{R}|, \verb|\pmancc{R}| & The ancestral and its converse. \\
+ $\pmrst{R}$, $\pmrts{R}$ & \verb|\pmrst{R}|, \verb|\pmrts{R}| & The powers of the ancestral and its converse. \\
+ $\pmmin{P}$, $\pmmax{P}$ & \verb|\pmmin{P}|, \verb|\pmmax{P}| & The minimum and maximum under $P$. \\
+ $\pmpot{R}$, $\pmpotid{R}$ & \verb|\pmpot{R}|, \verb|\pmpotid{R}| & The products (strict and not) of an ancestral. \\
+ $\pmpo{R}$ & \verb|\pmpo{R}| & The product of a class of ancestrals $R$. \\
+ $\pmB$ & \verb|\pmB| & The relation of beginning under $P$. \\
+ $\pmgen{P}$ & \verb|\pmgen{P}| & The generation of $P$. \\
+ $\pmefr{P}{Q}$ & \verb|\pmefr{P}{Q}| & The equi-factor relation. \\
+ $\pmipr{R}{x}$ & \verb|\pmipr{R}{x}| & The non-distinct posterity of $x$ under $R$. \\
+ $\pmjpr{R}{x}$ & \verb|\pmjpr{R}{x}| & The distinct posterity of $x$ under $R$. \\
+ $\pmfr{R}{x}$ & \verb|\pmfr{R}{x}| & The ancestry and posterity of $x$ under $R$. \\
+ $\pmnc{\kappa}$, $\pmNc$ & \verb|\pmnc{\kappa}|, \verb|\pmNc| & The cardinal number of $\kappa$.
\end{tabular}
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