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diff --git a/macros/latex/contrib/principia/principia.tex b/macros/latex/contrib/principia/principia.tex
index 76618c0b0b..86d5ce3a22 100644
--- a/macros/latex/contrib/principia/principia.tex
+++ b/macros/latex/contrib/principia/principia.tex
@@ -1,11 +1,13 @@
\documentclass[12pt]{article}
\NeedsTeXFormat{LaTeX2e}
-\ProvidesPackage{principia}[2020/10/25 principia package version 1.1] %This package supports typesetting the Peanese notation in Volume I of Whitehead and Russell’s 1910 ``Principia Mathematica".
+\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.
%Version 1.0 (superseded by Version 1.1): Covers typesetting of notation through Volume I. 2020/10/24
-%Version 1.1 (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
-%Version 1.2 (updates): boldfaced (`thickened') the truth-functional connectives, existential quantifier, set and relation symbols; added numerous commands for typesetting brackets and substitutions into theorems. 2021/02/23
+%Version 1.1 (superseded by Version 1.2) minor updates: fixed the spacing of scope dots around parentheses; fixed spacing of theorem sign; fixed spacing around primitive proposition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.
-%Copyright Landon D. C. Elkind, 2020. (https://landondcelkind.com/contact/).
+%Version 1.2 (superseded by Version 1.3) (minor updates): boldfaced (`thickened') the truth-functional connectives, existential quantifier, set and relation symbols; added numerous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
+%Licensed under LaTeX Project Public License 1.3c.
+%Copyright Landon D. C. Elkind, 2021. (https://landondcelkind.com/contact/).
\usepackage{fullpage}
\usepackage[T1]{fontenc}
@@ -13,14 +15,89 @@
\usepackage{setspace}
%Principia package requirements
-\usepackage{principia} %The package itself, and its dependencies:
\usepackage{amssymb} %This loads the relation domain and converse domain limitation symbols.
\usepackage{amsmath} %This loads the circumflex, substitution into theorems, \text{}, \mathbf{}, \boldsymbol{}, \overleftarrow{}, \overrightarrow{}, etc.
\usepackage{pifont} %This loads the eight-pointed asterisk.
-\usepackage{marvosym} %This loads the male and female symbol.
\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.
-\title{\texttt{principia.sty }\\ A \LaTeXe \space Package for Typesetting Whitehead and Russell's \textit{Principia Mathematica} (Version 1.2)}
+%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
+
+\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}}
\date{\today}
@@ -33,9 +110,11 @@ 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 1.2 (and 1.0-1.1) of \texttt{principia} is adequate to typeset all notations throughout Volume I of \textit{Principia} and includes some fixes to spacing, etc. See the package documentation for details. Updates to include all notations throughout Volumes II and III are planned.
+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.
+
+\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.
-\texttt{principia}'s dependencies are \texttt{amsmath}, \texttt{amssymb}, \texttt{pifont}, \texttt{marvosym}, and \texttt{graphicx}. Make sure to load these package by typing \texttt{$\backslash$usepackage\{graphicx\}}, etc., into the document preamble. To load \texttt{principia}, type \texttt{$\backslash$usepackage\{principia\}} in the document's preamble.
+To load \texttt{principia}, type \texttt{$\backslash$usepackage\{principia\}} in the document's preamble.
\noindent \begin{tabular}{@{}p{3cm} | p{5cm} | p{8.25cm}}
\textbf{Symbol} & \textbf{\LaTeX command} & \textbf{Notes} \\ \hline
@@ -70,105 +149,7 @@ Version 1.2 (and 1.0-1.1) of \texttt{principia} is adequate to typeset all notat
\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. \\
- $\pmcls{z}{\psi z}$ & \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 $\kappa$.
+ $\pmexists$ & \verb|\pmexists| & Existence.
\end{tabular}
\end{document} \ No newline at end of file