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authorKarl Berry <karl@freefriends.org>2010-10-15 22:36:07 +0000
committerKarl Berry <karl@freefriends.org>2010-10-15 22:36:07 +0000
commit1df1829282a57c887b9dc8ceefc83905a3359252 (patch)
tree6e65173b049160fc7245a79c2a975a367bf1f9e7 /Master/texmf-dist/tex/latex/rec-thy
parent997de50715b1ee678641cc9f12b4cba4cf964c90 (diff)
new latex package rec-thy 1.0 (16oct10)
git-svn-id: svn://tug.org/texlive/trunk@20114 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/tex/latex/rec-thy')
-rw-r--r--Master/texmf-dist/tex/latex/rec-thy/rec-thy.sty927
1 files changed, 927 insertions, 0 deletions
diff --git a/Master/texmf-dist/tex/latex/rec-thy/rec-thy.sty b/Master/texmf-dist/tex/latex/rec-thy/rec-thy.sty
new file mode 100644
index 00000000000..414ba560a33
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/rec-thy/rec-thy.sty
@@ -0,0 +1,927 @@
+\NeedsTeXFormat{LaTeX2e}
+\newcommand*{\@curpack}{\@currname} %rec-thy.sty
+\newcommand*{\@packinfo}[1]{\PackageInfo{\@curpack}{#1}}
+\newcommand*{\recthy@strip}[1]{%\expandafter\newcommand{\csname #1\endcsname}{}% Makes sure arg isn't already a command
+\expandafter\edef\csname #1\endcsname{\expandafter\noexpand\csname @recthy@#1\endcsname}} %leaves us a command \arg defined to do \@recthy@arg
+\ProvidesPackage{\@curpack} [2010/10/14 v1.0 Provides commands for writing up recursion theory papers] %file name is package name
+
+
+\RequirePackage{suffix}
+\RequirePackage{ifmtarg}
+\RequirePackage{xifthen}
+\RequirePackage{xkeyval}
+\RequirePackage{undertilde}
+\RequirePackage{stmaryrd}
+\RequirePackage{amsmath}
+\RequirePackage{amssymb}
+\RequirePackage{marvosym}
+\DeclareMathAlphabet{\mathbrush}{T1}{pbsi}{xl}{n}
+
+\newcommand*{\PMG@arginit}{\let\@PMG@parenarg\@PMG@undefined\let\@PMG@braketarg\@PMG@undefined}
+
+\newcommand*{\@recthy@family}{\@currname.\@currext} %The default family for this package...filename.ext
+%Define boolean options true if option passed false otherwise
+\define@boolkeys{\@recthy@family}[recthy@]{nohyphenation,nomath,nodelim,nosets,noquants,nospaces,nostrings,notrees,nopair,nonames,nosetrels,noordinalnotations,nosyntax,nodegclasses,noforcing} %of form \ifrecthy@nosets etc...
+
+\AtEndOfPackage{
+\ifrecthy@nohyphenation
+ \@packinfo{No hyphenation loading.}
+\else
+\hyphenation{ra-tion-als ra-tion-al Harrington Slaman Cholak Knight Gerdes Lange}
+\fi
+}
+
+\newcommand*{\@recthy@abs}[1]{\lvert#1\rvert}
+\newcommand*{\@recthy@ensuretext}[1]{\ensuremath{\text{#1}}}
+\AtEndOfPackage{
+\ifrecthy@nomath
+ \@packinfo{No math loading.}
+\else
+ \@packinfo{math loading.}
+ \newcommand*{\eqdef}{\stackrel{\text{\tiny def}}{=}} %\newcommand*{\eqdef}{\ensuremath{=\limits_{\text{\tiny def}}}}
+ \newcommand*{\iffdef}{\stackrel{\text{\tiny def}}{\iff}}
+ \DeclareMathOperator{\aut}{Aut}
+ \DeclareMathOperator{\Ord}{Ord}
+
+ \newcommand*{\meet}{\mathbin{\wedge}}
+ \newcommand*{\join}{\mathbin{\vee}}
+ \newcommand*{\Meet}{\mathop{\bigwedge}}
+ \let\MnJoin=\Join
+ \renewcommand*{\Join}{\mathop{\bigvee}}
+ \recthy@strip{abs}
+ \DeclareMathOperator{\dom}{dom}
+ \DeclareMathOperator{\rng}{rng}
+ \newcommand*{\restr}[1]{\mathpunct{\restriction_{#1}}}
+ \newcommand*{\ordpair}[2]{\left( #1, #2 \right) }
+ %%%%%%%%Function commands
+ \newcommand*{\map}[2]{:#1\mapsto #2}
+ \newcommand*{\functo}[3]{#1\map{#2}{#3}}
+ \newcommand*{\compfunc}{\mathbin{\circ}}
+ \let\compose=\compfunc
+ \let\funcomp=\compfunc
+ \recthy@strip{ensuretext}
+\fi
+}
+
+
+
+% corner quotes From Sam Buss http://www.phil.cam.ac.uk/teaching_staff/Smith/LaTeX/resources/godelquotes.txt
+\newbox\@recthy@gnBoxA
+\newdimen\@recthy@gnCornerHgt
+\setbox\@recthy@gnBoxA=\hbox{$\ulcorner$}
+\global\@recthy@gnCornerHgt=\ht\@recthy@gnBoxA
+\newdimen\@recthy@gnArgHgt
+
+\newcommand{\@recthy@godelnum}[1]{%
+ \setbox\@recthy@gnBoxA=\hbox{$#1$}%
+ \@recthy@gnArgHgt=\ht\@recthy@gnBoxA%
+ \ifnum \@recthy@gnArgHgt<\@recthy@gnCornerHgt
+ \@recthy@gnArgHgt=0pt%
+ \else
+ \advance \@recthy@gnArgHgt by -\@recthy@gnCornerHgt%
+ \fi
+ \raise\@recthy@gnArgHgt\hbox{$\ulcorner$} \box\@recthy@gnBoxA %
+ \raise\@recthy@gnArgHgt\hbox{$\urcorner$}}
+
+
+
+\newcommand*{\@recthy@llangle}{\mathopen{\langle\!\langle}}
+\newcommand*{\@recthy@rrangle}{\mathclose{\rangle\!\rangle}}
+
+
+
+\AtEndOfPackage{
+\ifrecthy@nodelim
+ \@packinfo{No delimiters loading.}
+\else
+ \newcommand*{\godelnum}[1]{\@recthy@godelnum{#1}}
+ \let\cornerquote=\godelnum
+ \let\gcode=\godelnum
+ \recthy@strip{llangle}
+ \recthy@strip{rrangle}
+\fi
+}
+
+\newcommand*{\@recthy@re}{\@recthy@ensuretext{r.e.}}
+\newcommand*{\@recthy@ce}{\@recthy@ensuretext{c.e.}}
+\newcommand*{\@recthy@recursive}{\@recthy@ensuretext{recursive}}
+\newcommand*{\@recthy@computable}{\@recthy@ensuretext{computable}}
+\newcommand*{\@recthy@recursivelyEnumerable}{\@recthy@ensuretext{recursively enumerable}}
+\newcommand*{\@recthy@computablyEnumerable}{\@recthy@ensuretext{computably enumerable}}
+\newcommand*{\@recthy@Recursive}{\@recthy@ensuretext{Recursive}}
+\newcommand*{\@recthy@Computable}{\@recthy@ensuretext{Computable}}
+\newcommand*{\@recthy@RecursivelyEnumerable}{\@recthy@ensuretext{Recursively enumerable}}
+\newcommand*{\@recthy@ComputablyEnumerable}{\@recthy@ensuretext{Computably enumerable}}
+\newcommand*{\@recthy@REA}{\ensuremath{\text{REA}}}
+\WithSuffix\def\@recthy@REA[#1]{#1-\REA\relax}
+\newcommand*{\@recthy@CEA}{\ensuremath{\text{CEA}}}
+\WithSuffix\def\@recthy@CEA[#1]{#1-\CEA\relax}
+
+\AtEndOfPackage{
+\ifrecthy@nonames
+ \@packinfo{No names loading.}
+\else
+ \@packinfo{Names loading.}
+ \recthy@strip{re}
+ \recthy@strip{ce}
+ \recthy@strip{REA}
+ \recthy@strip{CEA}
+ \recthy@strip{recursive}
+ \recthy@strip{computable}
+ \recthy@strip{recursivelyEnumerable}
+ \recthy@strip{computablyEnumerable}
+ \recthy@strip{Recursive}
+ \recthy@strip{Computable}
+ \recthy@strip{RecursivelyEnumerable}
+ \recthy@strip{ComputablyEnumerable}
+\fi
+}
+
+\DeclareOptionX<\@recthy@family>{re}{%
+ \let\@recthy@ce=\@recthy@re
+ \let\@recthy@computable=\@recthy@recursive
+ \let\@recthy@computablyEnumerable=\@recthy@recursivelyEnumerable
+ \let\@recthy@ComputablyEnumerable=\@recthy@RecursivelyEnumerable
+ } %Make all references to ce change to re
+
+ \DeclareOptionX<\@recthy@family>{rea}{%
+ \let\@recthy@CEA=\@recthy@REA
+ }
+
+\DeclareOptionX<\@recthy@family>{ce}{%
+ \let\@recthy@re=\@recthy@ce
+ \let\@recthy@recursive=\@recthy@computable
+ \let\@recthy@recursivelyEnumerable=\@recthy@computablyEnumerable
+ \let\@recthy@RecursivelyEnumerable=\@recthy@ComputablyEnumerable
+ } %Make all references to re change to ce
+
+\DeclareOptionX<\@recthy@family>{cea}{%
+ \let\@recthy@REA=\@recthy@CEA
+ }
+% Set stuff
+
+\newcommand*{\@recthy@set}[2]{\ifthenelse{\isempty{#2}}{\left \{ #1 \right \}}{\left \{ #1 \middle | #2\right \}} }
+
+
+\newcommand*{\@recthy@card}[1]{\lvert#1\rvert}
+\newcommand*{\@recthy@union}{\mathbin{\cup}}
+\newcommand*{\@recthy@Union}{\mathop{\bigcup}}
+\newcommand*{\@recthy@isect}{\mathbin{\cap}}
+\newcommand*{\@recthy@Isect}{\mathop{\bigcap}}
+
+\newcommand*{\@recthy@powset}[1]{\mathcal{P}\left(#1\right)}
+\newcommand*{\@recthy@eset}{\emptyset}
+\newcommand*{\@recthy@nin}{\mathrel{\not\in}}
+\newcommand*{\@recthy@setcmpminusSYM}{\backsim}
+\newcommand*{\@recthy@setminuscmp}[1]{\mathop{\@recthy@setcmpminusSYM} #1}
+\newcommand*{\@recthy@setovercmp}[1]{\overline{#1}}
+\let\@recthy@setcmp=\@recthy@setovercmp
+\def\@recthy@setminusSYM{-}
+
+
+\DeclareOptionX<\@recthy@family>{setminussym}{\def\@recthy@setminusSYM{#1}}
+\DeclareOptionX<\@recthy@family>{setcmpminussym}{\def\@recthy@setminusSYM{#1}}
+\DeclareOptionX<\@recthy@family>{minussetcmp}{\let\@recthy@setcmp=\@recthy@setminuscmp}
+\newcommand*{\@recthy@setminus}{\mathbin{\@recthy@setminusSYM}}
+
+
+
+\AtEndOfPackage{
+\WithSuffix\def\@recthy@setcmp[#1]#2{#1\@recthy@setminus#2}
+\ifrecthy@nosets
+ \@packinfo{No set cmds loading.}
+\else
+ \@packinfo{Set cmds loading.}
+ \recthy@strip{set}
+ \recthy@strip{card}
+ \recthy@strip{union}
+ \recthy@strip{Union}
+ \recthy@strip{isect}
+ \recthy@strip{Isect}
+ \recthy@strip{powset}
+ \recthy@strip{eset}
+ \recthy@strip{nin}
+ \recthy@strip{setcmp}
+ \recthy@strip{setovercmp}
+ \recthy@strip{setminuscmp}
+ \recthy@strip{setminus}
+ \newcommand*{\cross}{\mathbin{\times}}
+ \let\CrossOrig=\Cross
+ \def\Cross{}
+ \renewcommand*{\Cross}{\mathop{\Pi}}
+ \newcommand*{\symdiff}{\mathbin{\Delta}}
+ \DeclareMathOperator{\interior}{int}
+ \DeclareMathOperator{\closure}{cl}
+\fi
+}
+
+\AtEndOfPackage{
+\ifrecthy@noquants
+ \@packinfo{No quants loading.}
+\else
+ \@packinfo{Quants loading.}
+ \WithSuffix\def\exists(#1){\left(\exists\, #1 \right)\!}
+ \WithSuffix\def\forall(#1){\left(\forall\, #1 \right)\!}
+ \WithSuffix\def\nexists(#1){\left(\nexists\, #1 \right)\!}
+ \WithSuffix\def\exists[#1]{\left[\exists\, #1 \right]\!}
+ \WithSuffix\def\forall[#1]{\left[\forall\, #1 \right]\!}
+ \WithSuffix\def\nexists[#1]{\left[\nexists\, #1 \right]\!}
+ \WithSuffix\def\forall*{\forallae}
+ \WithSuffix\def\exists*{\existsinf}
+ \WithSuffix\def\nexists*{\nexistsinf}
+
+ \newcommand*{\forallae}{\forall^{*}}
+ \WithSuffix\def\forallae(#1){\left(\forallae\, #1\right)\!}
+ \WithSuffix\def\forallae[#1]{\left[\forallae\, #1\right]\!}
+ \newcommand*{\existsinf}{\exists^{\infty}}
+ \WithSuffix\def\existsinf(#1){\left(\existsinf\, #1\right)\!}
+ \WithSuffix\def\existsinf[#1]{\left[\existsinf\, #1\right]\!}
+ \newcommand*{\nexistsinf}{\nexists^{\infty}}
+ \WithSuffix\def\nexistsinf(#1){\left(\nexistsinf\, #1\right)\!}
+ \WithSuffix\def\nexistsinf[#1]{\left[\nexistsinf\, #1\right]\!}
+
+ \newcommand*{\True}{\top}
+ \newcommand*{\False}{\bot}
+
+ \newcommand*{\Land}{\mathop{\bigwedge}}
+ \newcommand*{\Lor}{\mathop{\bigvee}}
+ \newcommand*{\LLand}{\mathop{\bigwedge\mkern-15mu\bigwedge}}
+ \newcommand*{\LLor}{\mathop{\bigvee\mkern-15mu\bigvee}}
+
+ \newcommand*{\liff}{\ensuremath{\leftrightarrow}}
+ \newcommand*{\limplies}{\ensuremath{\rightarrow}}
+\fi
+}
+
+\AtEndOfPackage{
+\ifrecthy@nospaces
+ \@packinfo{No spaces loading.}
+\else
+ \@packinfo{Spaces loading.}
+
+ \newcommand*{\bstrs}{2^{<\omega}}
+ \newcommand*{\wstrs}{\omega^{<\omega}}
+
+ \newcommand*{\cantor}{2^{\omega}}
+ % \WithSuffix\def\cantor*{\left(2\union \diverge \right)^{\omega}}
+ \newcommand*{\baire}{\omega^{\omega}}
+ % \WithSuffix\def\baire*{\left(\omega \union \diverge \right)^{\omega}}
+ \newcommand*{\Baire}{\mathcal{N}}
+\fi
+}
+
+
+% \newcommand*{\recfnlSYM}{\Phi}
+%
+% \DeclareOptionX{recfn}{\def\recfnlSYM{#1}}
+
+
+%Strings
+
+\newcommand*{\@recthy@EmptyStr}{\str{}}
+\newcommand*{\@recthy@concatSYM}{\hat{}}
+\DeclareOptionX<\@recthy@family>{emptystr}[]{\def\@recthy@EmptyStr{#1}}
+\DeclareOptionX<\@recthy@family>{concat}[]{\def\@recthy@concatSYM{#1}}
+
+
+\AtEndOfPackage{
+\ifrecthy@nostrings
+ \@packinfo{No strings loading.}
+\else
+ \@packinfo{Strings loading.}
+
+ \newcommand*{\str}[1]{\mathopen{\@recthy@llangle}#1\mathclose{\@recthy@rrangle}}
+ \newcommand*{\code}{\str}
+ \newcommand*{\EmptyStr}{\@recthy@EmptyStr}
+ \newcommand*{\estr}{\EmptyStr}
+ \newcommand*{\decode}[2]{(#1)_{#2}}
+ \newcommand*{\godelpair}[2]{\mathopen{\langle} #1, #2 \mathclose{\rangle}}
+ \newcommand*{\gpair}{\godelpair}
+ \newcommand*{\concat}{\mathbin{\@recthy@concatSYM}}
+ \WithSuffix\def\concat[#1]{\concat\str{#1}}
+ \newcommand*{\strpred}[1]{{#1}^{-}}
+ \newcommand*{\lh}[2][]{\@recthy@abs{#2}_{#1}} %% Gives length of a string
+ \newcommand*{\incompat}{\mathrel{\mid}} %incompatible stringes FIX SPACING
+ \newcommand*{\incomp}{\incompat}
+ \newcommand*{\compat}{\mathrel{\nmid}}
+ \newcommand*{\setcol}[2]{{#1}^{[#2]}}
+ \ifrecthy@nopair
+ \@packinfo{No redefining pair.}
+ \else
+ \@packinfo{pair=godelpair.}
+ \newcommand*{\pair}{\godelpair}
+ \fi
+\fi
+}
+
+\AtEndOfPackage{
+\ifrecthy@notrees
+ \@packinfo{No trees loading.}
+\else
+ \@packinfo{Trees loading.}
+ \newcommand*{\CBderiv}[2][1]{#2^{\langle#1\rangle}}
+ \newcommand*{\pruneTree}[1]{\CBderiv[\infty]{#1}}
+ \newcommand*{\hgt}[1]{\lVert #1 \rVert}
+\fi
+}
+
+
+
+
+
+% Tree arguments
+
+% \newcommand*{\truepath}[2][]{\Gamma_{#1}\ifthenelse{\isempty{#2}}{}{(#2)}}
+% \newcommand*{\Tpath}{\truepath}
+
+%%%%%%
+\newcommand*{\murec}[2]{\ensuremath{\mu#1\left( #2 \right) }}
+
+%\newcommand*{\brecfSYM}{\phi}
+\newcommand*{\recfnlSYM}{\Phi}
+% \newcommand*{\recf}[3][]{\recfSYM^{#1}_{#2}\ifthenelse{\isempty{#3}}{}{\left(#3\right)}} %If give an empty arg just print function no parens
+%\newcommand*{\brecf}[3][]{\brecfSYM^{#1}_{#2}\ifthenelse{\isempty{#3}}{}{\left(#3\right)}}
+%\recfnl[d]{i}{Y}{x} gives i-th d-recursive functional operating on set Y and integer x
+\newcommand*{\recfnl}[4][]{\recfnlSYM_{#2\ifthenelse{\isempty{#1}}{}{,#1} }%
+ \ifthenelse{\isempty{#4}}%
+ {\ifthenelse{\isempty{#3}}%
+ {}% No args then print no parents
+ {(#3)}
+ }%If no oracle we just refer to the functional without any arguments
+ {\ifthenelse{\isempty{#3}}{(#4)}{(#3;#4)}%
+}}
+
+
+\newcommand*{\cequiv}{\mathrel{\backsimeq}}
+\newcommand*{\ncequiv}{\mathrel{\not\cequiv}}
+\newcommand*{\conv}[1][]{\mathpunct{\downarrow}_{#1}}
+%\newcommand*{\convs}[1]{\ensuremath{\conv_{#1}}}
+\newcommand*{\nconv}[1][]{\mathpunct{\mkern-4mu{\arrownot\mkern 4mu \downarrow}_{#1}}}
+\newcommand*{\diverge}{\mathpunct{\uparrow}}
+% \newcommand*{\use}[2]{\mathscr{u}(#1\ifthenelse{\isempty{#2}}{}{,#2})}
+\newcommand*{\use}[1]{\mathop{\mathbrush{u}}\!\left[{#1}\right]}
+
+\newcommand*{\REset}{\let\@PMG@parenarg\@PMG@undefined\let\@PMG@braketarg\@PMG@undefined\@REsetbody}
+\newcommand*{\@REsetbody}[1]{W\ifdefined\@PMG@parenarg
+^{\@PMG@parenarg}%
+\fi%
+\ifdefined\@PMG@braketarg
+_{#1, {\@PMG@braketarg}}%
+\else
+_{#1}
+\fi}
+\WithSuffix\def\@REsetbody(#1){\def\@PMG@parenarg{#1}\@REsetbody}
+\WithSuffix\def\@REsetbody[#1]{\def\@PMG@braketarg{#1}\@REsetbody}
+\newcommand*{\alphaREAop}[2][]{\mathcal{J}^{#2}_{#1}}
+\let\aREAop=\alphaREAop
+\let\reaop=\alphaREAop
+\newcommand*{\oneREAop}[1]{J_{#1}}
+\let\iREAop=\oneREAop
+\WithSuffix\def\reaop*#1{\oneREAop{#1}}
+%converges
+
+%%Computational Classes
+
+
+
+%%%%%%Turing Degrees
+\newcommand*{\Tdeg}[1]{\utilde{#1}}
+
+\newcommand*{\Tjump}[1]{#1'}
+\let\jump=\Tjump
+\newcommand*{\jumpn}[2]{#1^{(#2)}}
+\newcommand*{\jjump}[1]{#1''}
+% \newcommand*{\Tzerosym}{\MVZero}
+\newcommand*{\Tzerosym}{\MVZero}
+\newcommand*{\Tzero}{{\Tzerosym}}
+\newcommand*{\zeron}[1]{{\Tzerosym}^{(#1)}}
+\newcommand*{\zeroj}{\jump{{\Tzerosym}}}
+\let\Tzeroj=\zeroj
+\newcommand*{\zerojj}{\jump{\jump{{\Tzerosym}}}}
+\newcommand*{\zerojjj}{\jump{\jump{\jump{{\Tzerosym}}}}}
+\let\Tzerojj=\zerojj
+\let\Tzerojjj=\zerojjj
+
+%%Misc Recursion theory stuff
+%turing equivalent
+\newcommand*{\@recthy@TSYM}{\mathbf{T}}
+\newcommand*{\Tequiv}{\mathrel{\equiv_{\@recthy@TSYM}}}
+\newcommand*{\Teq}{\Tequiv}
+\newcommand*{\nTequiv}{\mathrel{\ncong_{\@recthy@TSYM}}}
+\newcommand*{\nTeq}{\nTequiv}
+%turing below
+
+\newcommand*{\Tlneq}{\lneq_{\@recthy@TSYM}}
+\newcommand*{\Tleq}{\leq_{\@recthy@TSYM}}
+\newcommand*{\Tgneq}{\gneq_{\@recthy@TSYM}}
+\newcommand*{\Tgeq}{\geq_{\@recthy@TSYM}}
+\newcommand*{\Tgtr}{>_{\@recthy@TSYM}}
+\newcommand*{\Tless}{<_{\@recthy@TSYM}}
+\newcommand*{\nTleq}{\nleq_{\@recthy@TSYM}}
+\newcommand*{\nTgeq}{\ngeq_{\@recthy@TSYM}}
+
+\newcommand*{\Tdegjoin}{\mathbin{\vee_{\@recthy@TSYM}}}
+\newcommand*{\Tdegmeet}{\mathbin{\wedge_{\@recthy@TSYM}}}
+\newcommand*{\Tmeet}{\Tdegmeet}
+\newcommand*{\Tsetjoin}{\mathbin{\oplus}}
+\newcommand*{\TsetJoin}{\mathop{\bigoplus}}
+\newcommand*{\Tplus}{\Tsetjoin}
+\newcommand*{\TPlus}{\TsetJoin}
+\newcommand*{\Tjoin}{\Tsetjoin}
+\newcommand*{\TJoin}{\TsetJoin}
+
+\DeclareOptionX<\@recthy@family>{degjoin}{\def\Tjoin{\Tdegjoin}}
+
+
+
+
+\newcommand*{\@recthy@ttSYM}{\ensuremath{\text{\tiny tt}}}
+\newcommand*{\ttSYM}{\@recthy@ttSYM}
+\newcommand*{\ttlneq}{\lneq_{\@recthy@ttSYM}}
+\newcommand*{\ttleq}{\leq_{\@recthy@ttSYM}}
+\newcommand*{\ttgneq}{\gneq_{\@recthy@ttSYM}}
+\newcommand*{\ttgeq}{\geq_{\@recthy@ttSYM}}
+\newcommand*{\ttgtr}{>_{\@recthy@ttSYM}}
+\newcommand*{\ttless}{<_{\@recthy@ttSYM}}
+\newcommand*{\ttTleq}{\nleq_{\@recthy@ttSYM}}
+\newcommand*{\ttTgeq}{\ngeq_{\@recthy@ttSYM}}
+
+
+
+%re set relations
+\AtEndOfPackage{
+\ifrecthy@nosetrels
+ \@packinfo{No setrels loading.}
+\else
+ \@packinfo{setrels loading.}
+
+ \WithSuffix\def\subset*{\subset^{*}}
+ \WithSuffix\def\supset*{\supset^{*}}
+ \WithSuffix\def\subseteq*{\subseteq^{*}}
+ \WithSuffix\def\supseteq*{\supseteq^{*}}
+ % \WithSuffix\def\subsetneq*{\subsetneq^{*}}
+ % \WithSuffix\def\supsetneq*{\supsetneq^{*}}
+ \providecommand*{\nsupset}{\not\supset}
+ \providecommand*{\nsubset}{\not\subset}
+ \newcommand*{\eq}{=}
+ \WithSuffix\def\eq*{=^{*}}
+ \newcommand*{\eqae}{=^{*}}
+
+
+ \newcommand*{\infsubset}{\subset_{\infty}}
+ \WithSuffix\def\infsubset*{\infsubset^{*}}
+ \let\subsetnaeq=\infsubset
+ \newcommand*{\infsupset}{\supset_{\infty}}
+ \WithSuffix\def\infsupset*{\infsupset^{*}}
+ \let\supsetnaeq=\infsupset
+ \newcommand*{\majsubset}{\subset_{m}}
+ \newcommand*{\majsupset}{\supset_{m}}
+\fi
+}
+
+
+
+
+
+
+
+
+
+
+
+%%% ORdinal notations
+% constructive/recursive ordinals
+
+\AtEndOfPackage{
+\ifrecthy@noordinalnotations
+ \@packinfo{No ordinal notations loading.}
+\else
+ \@packinfo{ordinal notations loading.}
+
+\newcommand*{\wck}{\ensuremath{\omega^{ck}_1}}
+ % \newcommand*{\ordtype}[1]{\ensuremath{\@recthy@abs{#1}_{\kleeneO}}}
+ \newcommand*{\ordzero}{\ensuremath{0}}
+
+ \newcommand*{\kleeneO}{\let\@PMG@parenarg\@PMG@undefined\let\@PMG@braketarg\@PMG@undefined\def\kleeneOSYM{\mathcal{O}}\@kleeneObody}
+ \newcommand*{\@kleeneObody}{\kleeneOSYM\ifdefined\@PMG@parenarg
+ ^{\@PMG@parenarg}%
+ \fi%
+ \ifdefined\@PMG@braketarg
+ _{\abs{\@PMG@braketarg}}%
+ \fi}
+ \WithSuffix\def\@kleeneObody(#1){\def\@PMG@parenarg{#1}\@kleeneObody}
+ \WithSuffix\def\@kleeneObody[#1]{\def\@PMG@braketarg{#1}\@kleeneObody}
+ \WithSuffix\def\@kleeneObody*{\def\kleeneOSYM{\overline{\mathcal{O}}}\@kleeneObody}
+
+
+ \newcommand*{\kleeneOuniq}{\kleeneO*}
+ \let\ordNotations=\kleeneO
+ \let\uniqOrdNotations=\kleeneOuniq
+ \newcommand*{\kleeneless}[1][]{<_{\kleeneO\ifthenelse{\isempty{#1}}{}{,#1}}}
+ \let\kleenel=\kleeneless
+ \newcommand*{\kleeneleq}[1][]{\leq_{\kleeneO\ifthenelse{\isempty{#1}}{}{,#1}}}
+ \newcommand*{\kleenenless}[1][]{\nless_{\kleeneO\ifthenelse{\isempty{#1}}{}{,#1}}}
+ \let\kleenenl=\kleenenless
+ \newcommand*{\kleenenleq}[1][]{\nleq_{\kleeneO\ifthenelse{\isempty{#1}}{}{,#1}}}
+ \newcommand*{\kleenegtr}[1][]{>_{\kleeneO\ifthenelse{\isempty{#1}}{}{,#1}}}
+ \let\kleeneg=\kleenegtr
+ \newcommand*{\kleenegeq}[1][]{\geq_{\kleeneO\ifthenelse{\isempty{#1}}{}{,#1}}}
+ \newcommand*{\kleenengtr}[1][]{\ngtr_{\kleeneO\ifthenelse{\isempty{#1}}{}{,#1}}}
+ \let\kleeneng=\kleenengtr
+ \newcommand*{\kleenengeq}[1][]{\ngeq_{\kleeneO\ifthenelse{\isempty{#1}}{}{,#1}}}
+ \newcommand*{\kleenePlus}{\mathbin{+_{\kleeneO}}}
+ \newcommand*{\kleeneMul}{\cdot_{\kleeneO}}
+ \newcommand*{\kleenehgt}[1]{\lVert #1\rVert_{\kleeneO}}
+ \let\hgtO=\kleenehgt
+ \newcommand*{\kleenelim}[2]{{#1}_{[#2]}}
+ \newcommand*{\kleenepred}[1]{{#1}^{-}}
+
+\fi
+}
+
+
+
+
+% \newcommand*{\axiom}{2}{#1}
+%alpha REA stuff
+% \newcommand*{\alphaREA}[1][\alpha]{\ensuremath{ #1 \text{-REA}} }
+
+
+\newcommand*{\@PMG@VdashStar}{{\Vdash\smash{\mkern-12mu\raise4\p@\hbox{\text{\tiny*}}}\mkern2mu}}
+
+% Forcing
+\AtEndOfPackage{
+\ifrecthy@noforcing
+ \@packinfo{No forcing loading.}
+\else
+ \@packinfo{forcing loading.}
+ \newcommand*{\forces}{\def\@PMG@frcparenarg{}\def\@PMG@frcbraketarg{}\def\@PMG@curfrcsym{\Vdash}\@forcesBody}
+ \newcommand*{\@forcesBody}{\mathrel{{\@PMG@curfrcsym}^{\@PMG@frcparenarg}_{\@PMG@frcbraketarg}}}
+ \WithSuffix\def\@forcesBody(#1){\def\@PMG@frcparenarg{#1}\@forcesBody}
+ \WithSuffix\def\@forcesBody[#1]{\def\@PMG@frcbraketarg{#1}\@forcesBody}
+ \WithSuffix\def\@forcesBody*{\let\@PMG@curfrcsym=\@PMG@VdashStar\@forcesBody}
+
+ % \long\def\forces@[#1][#2]{\Vdash^{#2}_{#1}}
+ % \newcommand{\forces}{\optparams{\forces@}{[][]}%
+ % }
+ \newcommand*{\frc}{\forces}
+\fi
+}
+
+
+%%%%%%%%% Formula Classes
+
+\newcommand*{\@recthy@CDelta}{\vphantom{\Delta}^{\mathcal{C}}\Delta}
+\newcommand*{\@recthy@CSigma}{\vphantom{\Sigma}^{\mathcal{C}}\Sigma}
+\newcommand*{\@recthy@CPi}{\vphantom{\Pi}^{\mathcal{C}}\Pi}
+\newcommand*{\@PMG@syntax}{\@PMG@synsym
+
+}
+
+\DeclareOptionX<\@recthy@family>{cdeltasym}{\def\@recthy@CDelta{#1}}
+\DeclareOptionX<\@recthy@family>{csigmasym}{\def\@recthy@CSigma{#1}}
+\DeclareOptionX<\@recthy@family>{cpisym}{\def\@recthy@CPi{#1}}
+
+\AtEndOfPackage{
+\ifrecthy@nosyntax
+ \@packinfo{No syntax loading.}
+\else
+ \@packinfo{syntax loading.}
+ \recthy@strip{CDelta}
+ \recthy@strip{CSigma}
+ \recthy@strip{CPi}
+ \newcommand*{\deltan}[1]{\Delta_{#1}}
+ \WithSuffix\def\deltan[#1]#2{\Delta^{#1}_{#2}}
+ % \WithSuffix\def\deltan(#1)#2{\deltan{#2}\!\left(#1\right)}
+ \newcommand*{\deltaZeroN}[1]{\Delta^{0}_{#1}}
+ \WithSuffix\def\deltaZeroN[#1]#2{\Delta^{0,#1}_{#2}}
+ % \WithSuffix\def\deltaZeroN(#1)#2{\deltaZeroN{#2}\!\left(#1\right)}
+ \newcommand*{\deltaZeroTwo}{\deltaZeroN{2}}
+ \WithSuffix\def\deltaZeroTwo[#1]{\deltaZeroN[#1]{2}}
+ % \WithSuffix\def\deltaZeroTwo(#1){\deltaZeroN[#1]{2}}
+ \newcommand*{\deltaZeroThree}{\deltaZeroN{3}}
+ \WithSuffix\def\deltaZeroThree[#1]{\deltaZeroN[#1]{3}}
+ % \WithSuffix\def\deltaZeroThree(#1){\deltaZeroN[#1]{3}}
+ \newcommand*{\deltaZeroOne}{\deltaZeroN{1}}
+ \WithSuffix\def\deltaZeroOne[#1]{\deltaZeroN[#1]{1}}
+ % \WithSuffix\def\deltaZeroOne(#1){\deltaZeroN[#1]{1}}
+ \newcommand*{\deltaZeroZero}{\deltaZeroN{0}}
+ \WithSuffix\def\deltaZeroZero[#1]{\deltaZeroN[#1]{0}}
+ % \WithSuffix\def\deltaZeroZero(#1){\deltaZeroN[#1]{0}}
+
+
+ \newcommand*{\deltaOneN}[1]{\deltan{#1}^1}
+ \WithSuffix\def\deltaOneN[#1]#2{\Delta^{1,#1}_{#2}}
+ % \WithSuffix\def\deltaOneN(#1)#2{\deltaOneN{#2}\!\left(#1\right)}
+ \newcommand*{\deltaOneOne}{\deltaOneN{1}}
+ \WithSuffix\def\deltaOneOne[#1]{\deltaOneN[#1]{1}}
+ % \WithSuffix\def\deltaOneOne(#1){\deltaOneN[#1]{1}}
+ \newcommand*{\deltaOneTwo}{\deltaOneN{2}}
+ \WithSuffix\def\deltaOneTwo[#1]{\deltaOneN[#1]{2}}
+ % \WithSuffix\def\deltaOneTwo(#1){\deltaOneN[#1]{2}}
+ \newcommand*{\deltaOneThree}{\deltaOneN{3}}
+ \WithSuffix\def\deltaOneThree[#1]{\deltaOneN[#1]{3}}
+ % \WithSuffix\def\deltaOneThree(#1){\deltaOneN[#1]{3}}
+
+
+
+ \newcommand*{\sigman}[1]{\Sigma_{#1}}
+ \WithSuffix\def\sigman[#1]#2{\Sigma^{#1}_{#2}}
+ % \WithSuffix\def\sigman(#1)#2{\sigman{#2}\!\left(#1\right)}
+ \newcommand*{\sigmaZeroN}[1]{\Sigma^{0}_{#1}}
+ \WithSuffix\def\sigmaZeroN[#1]#2{\Sigma^{0,#1}_{#2}}
+ % \WithSuffix\def\sigmaZeroN(#1)#2{\sigmaZeroN{#2}\!\left(#1\right)}
+ \newcommand*{\sigmaZeroOne}{\sigmaZeroN{1}}
+ \WithSuffix\def\sigmaZeroOne[#1]{\sigmaZeroN[#1]{1}}
+ % \WithSuffix\def\sigmaZeroOne(#1){\sigmaZeroN[#1]{1}}
+ \newcommand*{\sigmaZeroTwo}{\sigmaZeroN{2}}
+ \WithSuffix\def\sigmaZeroTwo[#1]{\sigmaZeroN[#1]{2}}
+ % \WithSuffix\def\sigmaZeroTwo(#1){\sigmaZeroN[#1]{2}}
+ \newcommand*{\sigmaZeroThree}{\sigmaZeroN{3}}
+ \WithSuffix\def\sigmaZeroThree[#1]{\sigmaZeroN[#1]{3}}
+ % \WithSuffix\def\sigmaZeroThree(#1){\sigmaZeroN[#1]{3}}
+
+
+
+ \newcommand*{\sigmaOneN}[1]{\Sigma^1_{#1}}
+ \WithSuffix\def\sigmaOneN[#1]#2{\Sigma^{1,#1}_{#2}}
+ % \WithSuffix\def\sigmaOneN(#1)#2{\sigmaOneN{#2}\!\left(#1\right)}
+ \newcommand*{\sigmaOneOne}{\sigmaOneN{1}}
+ \WithSuffix\def\sigmaOneOne[#1]{\sigmaOneN[#1]{1}}
+ % \WithSuffix\def\sigmaOneOne(#1){\sigmaOneN[#1]{1}}
+ \newcommand*{\sigmaOneTwo}{\sigmaOneN{2}}
+ \WithSuffix\def\sigmaOneTwo[#1]{\sigmaOneN[#1]{2}}
+ % \WithSuffix\def\sigmaOneTwo(#1){\sigmaOneN[#1]{2}}
+ \newcommand*{\sigmaOneThree}{\sigmaOneN{3}}
+ \WithSuffix\def\sigmaOneThree[#1]{\sigmaOneN[#1]{3}}
+ % \WithSuffix\def\sigmaOneThree(#1){\sigmaOneN[#1]{3}}
+
+
+
+ \newcommand*{\pin}[1]{\Pi_{#1}}
+ \WithSuffix\def\pin[#1]#2{\Pi^{#1}_{#2}}
+ % \WithSuffix\def\pin(#1)#2{\pin{#2}\!\left(#1\right)}
+ \newcommand*{\piZeroN}[1]{\Pi^0_{#1}}
+ \WithSuffix\def\piZeroN[#1]#2{\Pi^{0,#1}_{#2}}
+ % \WithSuffix\def\piZeroN(#1)#2{\piZeroN{#2}\left(#1\right)}
+ \newcommand*{\piZeroOne}{\piZeroN{1}}
+ \WithSuffix\def\piZeroOne[#1]{\piZeroN[#1]{1}}
+ % \WithSuffix\def\piZeroOne(#1){\piZeroN[#1]{1}}
+ \newcommand*{\piZeroTwo}{\piZeroN{2}}
+ \WithSuffix\def\piZeroTwo[#1]{\piZeroN[#1]{2}}
+ % \WithSuffix\def\piZeroTwo(#1){\piZeroN[#1]{2}}
+ \newcommand*{\piZeroThree}{\piZeroN{3}}
+ \WithSuffix\def\piZeroThree[#1]{\piZeroN[#1]{3}}
+ % \WithSuffix\def\piZeroThree(#1){\piZeroN[#1]{3}}
+
+ \newcommand*{\piOneN}[1]{\Pi^1_{#1}}
+ \WithSuffix\def\piOneN[#1]#2{\Pi^{1,#1}_{#2}}
+ % \WithSuffix\def\piOneN(#1)#2{\piOneN{#2}\!\left(#1\right)}
+ \newcommand*{\piOneOne}{\piOneN{1}}
+ \WithSuffix\def\piOneOne[#1]{\piOneN[#1]{1}}
+ % \WithSuffix\def\piOneOne(#1){\piOneN[#1]{1}}
+ \newcommand*{\piOneTwo}{\piOneN{2}}
+ \WithSuffix\def\piOneTwo[#1]{\piOneN[#1]{2}}
+ % \WithSuffix\def\piOneTwo(#1){\piOneN[#1]{2}}
+ \newcommand*{\piOneThree}{\piOneN{3}}
+ \WithSuffix\def\piOneThree[#1]{\piOneN[#1]{3}}
+ % \WithSuffix\def\piOneThree(#1){\piOneN[#1]{3}}
+
+
+
+ %%%ABREVIATIONS
+ \newcommand*{\deltaz}{\deltaN{0}}
+ \newcommand*{\deltazn}{\deltaZeroN}
+ \newcommand*{\deltazii}{\deltaZeroTwo}
+ \newcommand*{\deltazi}{\deltaZeroOne}
+ \newcommand*{\deltazz}{\deltaZeroZero}
+ \newcommand*{\deltaziii}{\deltaZeroThree}
+ \newcommand*{\deltaIn}{\deltaOneN}
+ \newcommand*{\deltaIi}{\deltaOneOne}
+ \newcommand*{\deltaoneone}{\deltaOneOne}
+ \newcommand*{\deltaIii}{\deltaOneTwo}
+ \newcommand*{\deltaIiii}{\deltaOneThree}
+ \newcommand*{\sigmazn}{\sigmaZeroN}
+ \newcommand*{\sigmazi}{\sigmaZeroOne}
+ \newcommand*{\sigmazii}{\sigmaZeroTwo}
+ \newcommand*{\sigmaziii}{\sigmaZeroThree}
+ \newcommand*{\sigmaIn}{\sigmaOneN}
+ \newcommand*{\sigmaIi}{\sigmaOneOne}
+ \newcommand*{\sigmaIii}{\sigmaOneTwo}
+ \newcommand*{\sigmaIiii}{\sigmaOneThree}
+ \newcommand*{\pizn}{\piZeroN}
+ \newcommand*{\pizi}{\piZeroOne}
+ \newcommand*{\pizii}{\piZeroTwo}
+ \newcommand*{\piziii}{\piZeroThree}
+ \newcommand*{\piIn}{\piOneN}
+ \newcommand*{\piIi}{\piOneOne}
+ \newcommand*{\piIii}{\piOneTwo}
+ \newcommand*{\piIiii}{\piOneThree}
+
+ %%%%%%%%%%%%%
+ % \newcommand*{\sigmapizn}[1]{\sigmazn{#1} \union \pizn{#1}}
+ % \WithSuffix\def\sigmapizn[#1]#2{\sigmazn[#1]{#2} \union \pizn[#1]{#2}}
+ % \WithSuffix\def\sigmapizn(#1)#2{\sigmazn[#1]{#2} \union \pizn[#1]{#2}}
+ % \let\pisigmazn=\sigmapizn
+ %%%%%%%%%%%%%%
+
+ %%%%%%%%
+ % Logics
+ %\newcommand*{\equiv}
+ \newcommand*{\logic}[2]{\mathcal{L}_{#1,#2}}
+ % \newcommand*{\logicwiw}{\logic{\omega_{1}}{\omega}}
+ % \newcommand*{\Clogic}[2]{\mathcal{CL}_{#1,#2}}
+ % \newcommand*{\FOlogic}{\logic{\omega}{\omega}}
+ % \newcommand*{\hyplogic}[1][]{\Clogic{\omega_{1}}{\omega}\ifthenelse{\isempty{#1}}{}{\left(#1\right)} }
+
+
+
+ %May never use...specific notation for computable formulas...supplanted by \( \sigmazn{\alpha} \) notation.
+ %%%%%%%%%%%
+
+
+
+
+
+ \newcommand*{\Cdeltan}[1]{\CDelta_{#1}}
+ \WithSuffix\def\Cdeltan[#1]#2{\Cdeltan{#2}^{#1}}
+ % \WithSuffix\def\Cdeltan(#1)#2{\Cdeltan{#2}\left(#1\right)}
+
+
+
+
+
+ \newcommand*{\Cpin}[1]{\CPi_{#1}}
+ \WithSuffix\def\Cpin[#1]#2{\Cpin{#2}^{#1}}
+ % \WithSuffix\def\Cpin(#1)#2{\Cpin{#2}\!\left(#1\right)}
+
+
+ \newcommand*{\Csigman}[1]{\CSigma_{#1}}
+ \WithSuffix\def\Csigman[#1]#2{\Csigman{#2}^{#1}}
+ % \WithSuffix\def\Csigman(#1)#2{\Csigman{#2}\!\left(#1\right)}
+
+%%%BOLDFACE
+
+ \newcommand*{\Deltan}[1]{\utilde{\mathbf{\Delta}}_{#1}}
+ \WithSuffix\def\Deltan[#1]#2{\utilde{\mathbf{\Delta}}^{#1}_{#2}}
+ % \WithSuffix\def\Deltan(#1)#2{\deltan{#2}\!\left(#1\right)}
+ \newcommand*{\DeltaZeroN}[1]{\utilde{\mathbf{\Delta}}^{0}_{#1}}
+ \WithSuffix\def\DeltaZeroN[#1]#2{\utilde{\mathbf{\Delta}}^{0,#1}_{#2}}
+ % \WithSuffix\def\DeltaZeroN(#1)#2{\DeltaZeroN{#2}\!\left(#1\right)}
+ \newcommand*{\DeltaZeroTwo}{\DeltaZeroN{2}}
+ \WithSuffix\def\DeltaZeroTwo[#1]{\DeltaZeroN[#1]{2}}
+ % \WithSuffix\def\DeltaZeroTwo(#1){\DeltaZeroN[#1]{2}}
+ \newcommand*{\DeltaZeroThree}{\DeltaZeroN{3}}
+ \WithSuffix\def\DeltaZeroThree[#1]{\DeltaZeroN[#1]{3}}
+ % \WithSuffix\def\DeltaZeroThree(#1){\DeltaZeroN[#1]{3}}
+ \newcommand*{\DeltaZeroOne}{\DeltaZeroN{1}}
+ \WithSuffix\def\DeltaZeroOne[#1]{\DeltaZeroN[#1]{1}}
+ % \WithSuffix\def\DeltaZeroOne(#1){\DeltaZeroN[#1]{1}}
+ \newcommand*{\DeltaZeroZero}{\DeltaZeroN{0}}
+ \WithSuffix\def\DeltaZeroZero[#1]{\DeltaZeroN[#1]{0}}
+ % \WithSuffix\def\DeltaZeroZero(#1){\DeltaZeroN[#1]{0}}
+
+
+ \newcommand*{\DeltaOneN}[1]{\Deltan{#1}^1}
+ \WithSuffix\def\DeltaOneN[#1]#2{\utilde{\mathbf{\Delta}}^{1,#1}_{#2}}
+ % \WithSuffix\def\DeltaOneN(#1)#2{\DeltaOneN{#2}\!\left(#1\right)}
+ \newcommand*{\DeltaOneOne}{\DeltaOneN{1}}
+ \WithSuffix\def\DeltaOneOne[#1]{\DeltaOneN[#1]{1}}
+ % \WithSuffix\def\DeltaOneOne(#1){\DeltaOneN[#1]{1}}
+ \newcommand*{\DeltaOneTwo}{\DeltaOneN{2}}
+ \WithSuffix\def\DeltaOneTwo[#1]{\DeltaOneN[#1]{2}}
+ % \WithSuffix\def\DeltaOneTwo(#1){\DeltaOneN[#1]{2}}
+ \newcommand*{\DeltaOneThree}{\DeltaOneN{3}}
+ \WithSuffix\def\DeltaOneThree[#1]{\DeltaOneN[#1]{3}}
+ % \WithSuffix\def\DeltaOneThree(#1){\DeltaOneN[#1]{3}}
+
+
+
+ \newcommand*{\Sigman}[1]{\utilde{\mathbf{\Sigma}}_{#1}}
+ \WithSuffix\def\Sigman[#1]#2{\utilde{\mathbf{\Sigma}}^{#1}_{#2}}
+ % \WithSuffix\def\Sigman(#1)#2{\sigman{#2}\!\left(#1\right)}
+ \newcommand*{\SigmaZeroN}[1]{\utilde{\mathbf{\Sigma}}^{0}_{#1}}
+ \WithSuffix\def\SigmaZeroN[#1]#2{\utilde{\mathbf{\Sigma}}^{0,#1}_{#2}}
+ % \WithSuffix\def\SigmaZeroN(#1)#2{\SigmaZeroN{#2}\!\left(#1\right)}
+ \newcommand*{\SigmaZeroOne}{\SigmaZeroN{1}}
+ \WithSuffix\def\SigmaZeroOne[#1]{\SigmaZeroN[#1]{1}}
+ % \WithSuffix\def\SigmaZeroOne(#1){\SigmaZeroN[#1]{1}}
+ \newcommand*{\SigmaZeroTwo}{\SigmaZeroN{2}}
+ \WithSuffix\def\SigmaZeroTwo[#1]{\SigmaZeroN[#1]{2}}
+ % \WithSuffix\def\SigmaZeroTwo(#1){\SigmaZeroN[#1]{2}}
+ \newcommand*{\SigmaZeroThree}{\SigmaZeroN{3}}
+ \WithSuffix\def\SigmaZeroThree[#1]{\SigmaZeroN[#1]{3}}
+ % \WithSuffix\def\SigmaZeroThree(#1){\SigmaZeroN[#1]{3}}
+
+
+
+ \newcommand*{\SigmaOneN}[1]{\utilde{\mathbf{\Sigma}}^1_{#1}}
+ \WithSuffix\def\SigmaOneN[#1]#2{\utilde{\mathbf{\Sigma}}^{1,#1}_{#2}}
+ % \WithSuffix\def\SigmaOneN(#1)#2{\SigmaOneN{#2}\!\left(#1\right)}
+ \newcommand*{\SigmaOneOne}{\SigmaOneN{1}}
+ \WithSuffix\def\SigmaOneOne[#1]{\SigmaOneN[#1]{1}}
+ % \WithSuffix\def\SigmaOneOne(#1){\SigmaOneN[#1]{1}}
+ \newcommand*{\SigmaOneTwo}{\SigmaOneN{2}}
+ \WithSuffix\def\SigmaOneTwo[#1]{\SigmaOneN[#1]{2}}
+ % \WithSuffix\def\SigmaOneTwo(#1){\SigmaOneN[#1]{2}}
+ \newcommand*{\SigmaOneThree}{\SigmaOneN{3}}
+ \WithSuffix\def\SigmaOneThree[#1]{\SigmaOneN[#1]{3}}
+ % \WithSuffix\def\SigmaOneThree(#1){\SigmaOneN[#1]{3}}
+
+
+
+ \newcommand*{\Pin}[1]{\utilde{\mathbf{\Pi}}_{#1}}
+ \WithSuffix\def\Pin[#1]#2{\utilde{\mathbf{\Pi}}^{#1}_{#2}}
+ % \WithSuffix\def\Pin(#1)#2{\pin{#2}\!\left(#1\right)}
+ \newcommand*{\PiZeroN}[1]{\utilde{\mathbf{\Pi}}^0_{#1}}
+ \WithSuffix\def\PiZeroN[#1]#2{\utilde{\mathbf{\Pi}}^{0,#1}_{#2}}
+ % \WithSuffix\def\PiZeroN(#1)#2{\PiZeroN{#2}\left(#1\right)}
+ \newcommand*{\PiZeroOne}{\PiZeroN{1}}
+ \WithSuffix\def\PiZeroOne[#1]{\PiZeroN[#1]{1}}
+ % \WithSuffix\def\PiZeroOne(#1){\PiZeroN[#1]{1}}
+ \newcommand*{\PiZeroTwo}{\PiZeroN{2}}
+ \WithSuffix\def\PiZeroTwo[#1]{\PiZeroN[#1]{2}}
+ % \WithSuffix\def\PiZeroTwo(#1){\PiZeroN[#1]{2}}
+ \newcommand*{\PiZeroThree}{\PiZeroN{3}}
+ \WithSuffix\def\PiZeroThree[#1]{\PiZeroN[#1]{3}}
+ % \WithSuffix\def\PiZeroThree(#1){\PiZeroN[#1]{3}}
+
+ \newcommand*{\PiOneN}[1]{\utilde{\mathbf{\Pi}}^1_{#1}}
+ \WithSuffix\def\PiOneN[#1]#2{\utilde{\mathbf{\Pi}}^{1,#1}_{#2}}
+ % \WithSuffix\def\PiOneN(#1)#2{\PiOneN{#2}\!\left(#1\right)}
+ \newcommand*{\PiOneOne}{\PiOneN{1}}
+ \WithSuffix\def\PiOneOne[#1]{\PiOneN[#1]{1}}
+ % \WithSuffix\def\PiOneOne(#1){\PiOneN[#1]{1}}
+ \newcommand*{\PiOneTwo}{\PiOneN{2}}
+ \WithSuffix\def\PiOneTwo[#1]{\PiOneN[#1]{2}}
+ % \WithSuffix\def\PiOneTwo(#1){\PiOneN[#1]{2}}
+ \newcommand*{\PiOneThree}{\PiOneN{3}}
+ \WithSuffix\def\PiOneThree[#1]{\PiOneN[#1]{3}}
+ % \WithSuffix\def\PiOneThree(#1){\PiOneN[#1]{3}}
+
+
+
+ %%%ABREVIATIONS
+ \newcommand*{\Deltaz}{\deltaN{0}}
+ \newcommand*{\Deltazn}{\DeltaZeroN}
+ \newcommand*{\Deltazii}{\DeltaZeroTwo}
+ \newcommand*{\Deltazi}{\DeltaZeroOne}
+ \newcommand*{\Deltazz}{\DeltaZeroZero}
+ \newcommand*{\Deltaziii}{\DeltaZeroThree}
+ \newcommand*{\DeltaIn}{\DeltaOneN}
+ \newcommand*{\DeltaIi}{\DeltaOneOne}
+ \newcommand*{\Deltaoneone}{\DeltaOneOne}
+ \newcommand*{\DeltaIii}{\DeltaOneTwo}
+ \newcommand*{\DeltaIiii}{\DeltaOneThree}
+ \newcommand*{\Sigmazn}{\SigmaZeroN}
+ \newcommand*{\Sigmazi}{\SigmaZeroOne}
+ \newcommand*{\Sigmazii}{\SigmaZeroTwo}
+ \newcommand*{\Sigmaziii}{\SigmaZeroThree}
+ \newcommand*{\SigmaIn}{\SigmaOneN}
+ \newcommand*{\SigmaIi}{\SigmaOneOne}
+ \newcommand*{\SigmaIii}{\SigmaOneTwo}
+ \newcommand*{\SigmaIiii}{\SigmaOneThree}
+ \newcommand*{\Pizn}{\PiZeroN}
+ \newcommand*{\Pizi}{\PiZeroOne}
+ \newcommand*{\Pizii}{\PiZeroTwo}
+ \newcommand*{\Piziii}{\PiZeroThree}
+ \newcommand*{\PiIn}{\PiOneN}
+ \newcommand*{\PiIi}{\PiOneOne}
+ \newcommand*{\PiIii}{\PiOneTwo}
+ \newcommand*{\PiIiii}{\PiOneThree}
+
+
+
+
+
+
+\fi
+}
+
+
+%%%ABREVIATIONS
+
+
+
+%Degree Classes
+\AtEndOfPackage{
+\ifrecthy@nodegclasses
+ \@packinfo{No degree classes loading.}
+\else
+ \@packinfo{Degree classes loading.}
+ \newcommand{\Low}[1][]{\ensuremath{ \text{Low}^{#1} }}
+ \newcommand{\LowN}[2][]{\ensuremath{ \text{Low}^{#1}_{#2} }}
+ \newcommand{\lowN}[2][]{\ensuremath{ \mathcal{L}^{#1}_{#2} }}
+ \newcommand{\req}[2]{\ensuremath{\mathcal{#1}_{#2}}}
+\fi
+}
+
+\ProcessOptionsX<\@recthy@family>
+
+
+
+
+
+
+
+