\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{rec-thy}[2017/12/31 v2.3  Provides commands for writing up recursion theory papers]
\makeatletter
% \newcommand*{\@curpack}{\@currname} %rec-thy.sty
\newcommand*{\@packinfo}[1]{\PackageInfo{rec-thy}{#1}}
\newcommand*{\recthy@strip}[1]{%
\ifcsname #1\endcsname%
\else%
\expandafter\edef\csname #1\endcsname{\expandafter\noexpand\csname @recthy@#1\endcsname}
\fi
}
%leaves us a command \arg defined to do \@recthy@arg
% \ProvidesPackage{\@curpack}  %file name is package name

% Release Notes
% Version 1.2
% Added mrref option
% Fixed horrific option processing bug
\RequirePackage{ltxcmds}
\RequirePackage{ifxetex,ifpdf}
\RequirePackage{suffix}
\RequirePackage{ifmtarg}
\RequirePackage{xifthen}
\RequirePackage{xkeyval}
\RequirePackage{etoolbox}
\robustify\(
\robustify\)
\RequirePackage{xparse}
\RequirePackage{ifxetex}
\AtBeginDocument{
\ltx@ifpackageloaded{amsmath}{}{\RequirePackage{amsmath}}
\ltx@ifpackageloaded{amssymb}{}{\RequirePackage{amssymb}}
\ltx@ifpackageloaded{amsfonts}{}{\RequirePackage{amsfonts}}
\ltx@ifpackageloaded{mathtools}{}{\RequirePackage{mathtools}}
\ltx@ifpackageloaded{unicode-math}{}{\RequirePackage{mathrsfs}}
\ltx@ifpackageloaded{undertilde}{}{\RequirePackage{undertilde}}
}

% \ifxetex  %workaround for bug...hopefully can dispense on later
% \gdef\symbf#1{\symbf{#1}}
% \fi
% \global\let\symbf=\symbf
\ifxetex
\else
    \def\symbf#1{\mathbf{#1}}
\fi



% \DeclareMathAlphabet{\mathbrush}{T1}{pbsi}{xl}{n}
% \newcommand*{\mathbrush}[1]{\mathsfit{#1}}
% \ifxetex
%   \RequirePackage{xltxtra}
%   \RequirePackage{unicode-math}
%   % \RequirePackage{fontspec,xunicode}
%   % \defaultfontfeatures{Mapping=tex-text,Scale=MatchLowercase} % To support LaTeX quoting style
%   % \input{/Users/TruePath/Library/texmf/tex/headers/appearence.tex}
% \else
%   % \usepackage[utf8]{inputenc}
%   % \usepackage[T1]{fontenc}
%   % \RequirePackage{euscript}
%   % \newcommand*{\matheu}{\EuScript}

%   \ifpdf
%   \RequirePackage{cmap} % you can search in the pdf for umlauts and ligatures
%   \fi
% \fi
% \RequirePackage{stmaryrd}
% \RequirePackage{marvosym}

\def\PMG@arginit{\let\@PMG@parenarg\@PMG@undefined\let\@PMG@braketarg\@PMG@undefined}

\def\@recthy@family{\@currname.\@currext} %The default family for this package...filename.ext
%Define boolean options true if option passed false otherwise


\newif\ifrecthy@nohyphenation       \recthy@nohyphenationfalse
\newif\ifrecthy@mrref           \recthy@mrreffalse
\newif\ifrecthy@nomath          \recthy@nomathfalse
\newif\ifrecthy@nodelim         \recthy@nodelimfalse
\newif\ifrecthy@nonames
\recthy@nonamesfalse
\newif\ifrecthy@nosets
\recthy@nosetsfalse
\newif\ifrecthy@noquants\recthy@noquantsfalse
\newif\ifrecthy@nospaces        \recthy@nospacesfalse
\newif\ifrecthy@nostrings       \recthy@nostringsfalse
\newif\ifrecthy@notrees         \recthy@notreesfalse
\newif\ifrecthy@nopair          \recthy@nopairfalse
\newif\ifrecthy@nonames         \recthy@nonamesfalse
\newif\ifrecthy@nosetrels       \recthy@nosetrelsfalse
\newif\ifrecthy@noordinalnotations  \recthy@noordinalnotationsfalse
\newif\ifrecthy@nosyntax        \recthy@nosyntaxfalse
\newif\ifrecthy@nodegclasses        \recthy@nodegclassesfalse
\newif\ifrecthy@noforcing       \recthy@noforcingfalse
\newif\ifrecthy@nodegrees       \recthy@nodegreesfalse
\newif\ifrecthy@nocomputations      \recthy@nocomputationsfalse
\newif\ifrecthy@nostructresets \recthy@nostructresetsfalse
\newif\ifrecthy@noreqhelper \recthy@noreqhelperfalse
\newif\ifrecthy@nosubfun \recthy@nosubfunfalse
\newif\ifrecthy@nopfcases \recthy@nopfcasesfalse
\newif\ifrecthy@noprioritytrees \recthy@noprioritytreesfalse
\newif\ifrecthy@hyperreqs \recthy@hyperreqstrue

\DeclareOptionX{nohyphenation}{\recthy@nohyphenationtrue}
\DeclareOptionX{mrref}{\recthy@mrreftrue}
\DeclareOptionX{nomath}{\recthy@nomathtrue}
\DeclareOptionX{nodelim}{\recthy@nodelimtrue}
\DeclareOptionX{nonames}{\recthy@nonamestrue}
\DeclareOptionX{nosets}{\recthy@nosetstrue}
\DeclareOptionX{noquants}{\recthy@noquantstrue}
\DeclareOptionX{nospaces}{\recthy@nospacestrue}
\DeclareOptionX{nostrings}{\recthy@nostringstrue}
\DeclareOptionX{notrees}{\recthy@notreestrue}
\DeclareOptionX{nopair}{\recthy@nopairtrue}
\DeclareOptionX{nosetrels}{\recthy@nosetrelstrue}
\DeclareOptionX{noordinalnotations}{\recthy@noordinalnotationstrue}
\DeclareOptionX{nosyntax}{\recthy@nosyntaxtrue}
\DeclareOptionX{nodegclasses}{\recthy@nodegclassestrue}
\DeclareOptionX{noforcing}{\recthy@noforcingtrue}
\DeclareOptionX{nodegrees}{\recthy@nodegreestrue}
\DeclareOptionX{nocomputations}{\recthy@nocomputationstrue}
\DeclareOptionX{nostructresets}{\recthy@nostructresetstrue}
\DeclareOptionX{noreqhelper}{\recthy@noreqhelpertrue}
\DeclareOptionX{nosubfun}{\recthy@nosubfuntrue}
\DeclareOptionX{nopfcases}{\recthy@nopfcasestrue}
\DeclareOptionX{noprioritytrees}{\recthy@noprioritytreestrue}
\DeclareOptionX{nohyperreqs}{\recthy@hyperreqsfalse}

\DeclareOptionX{degjoin}{\def\Tjoin{\Tdegjoin}}


\AtEndOfPackage{
    \ifrecthy@noprioritytrees
        \@packinfo{Not loading Priority Tree Helper}
    \else
        \@packinfo{Loading Priority Tree Helper.}
        \providecommand{\PriorityTree}{\mathbb{T}}
        \providecommand{\tpath}[1][]{\ifthenelse{\isempty{#1}}{\symbf{f}}{\mathbb{f}_{#1}}}
        \providecommand{\leftof}{\mathbin{<_L}}
        \providecommand{\ball}[3][]{{\ifdefined\symbf
                                        \symbf{\alpha}
                                      \else
                                        \alpha
                                      \fi}^{#1}(#2, #3)}
        \providecommand*{\Astages}[1]{\mathcal{S}_{\text{act}}^{#1}}
        \providecommand*{\Vstages}[1]{\mathcal{S}^{#1}}
        \providecommand{\reqof}[2][]{\mathbb{r}(#2)}
    \fi
}

\let\pmg@casefont=\textsc
\DeclareOptionX{pfcasefont}{\edef\pmg@casefont{\expandafter\noexpand\csname #1 \endcsname}}

\AtEndOfPackage{
    \ifrecthy@nopfcases
        \@packinfo{Not loading Proof Cases Helper}
    \else
        \@packinfo{Loading Proof Cases Helper.}
        \RequirePackage{enumitem}
        \ltx@ifpackageloaded{cleveref}{
        \crefformat{pfcasesnonumi}{#2case~#1#3}
        \Crefformat{pfcasesnonumi}{#2Case~#1#3}
        \crefformat{pfcasesnonumii}{#2subcase~#1#3}
        \Crefformat{pfcasesnonumii}{#2Subcase~#1#3}
        \crefformat{pfcasesnonumiii}{#2subsubcase~#1#3}
        \Crefformat{pfcasesnonumiii}{#2Subsubcase~#1#3}
        \crefformat{pfcasesnumberedi}{#2case~#1#3}
        \Crefformat{pfcasesnumberedi}{#2Case~#1#3}
        \crefformat{pfcasesnumberedii}{#2case~#1#3}
        \Crefformat{pfcasesnumberedii}{#2Case~#1#3}
        \crefformat{pfcasesnumberediii}{#2case~#1#3}
        \Crefformat{pfcasesnumberediii}{#2Case~#1#3}
        }{}
        \newlist{pfcasesnonum}{enumerate}{3}
        \setlist[pfcasesnonum]{
          label={\pmg@casefont{Case}}\protect\thiscase:~,
          align=left,
          labelsep=!,
          itemindent=-1em,
          leftmargin=2em,
          labelindent=0pt,
          labelwidth=0pt
        }
        \setlist[pfcasesnonum,1]{
            before=\def\pfcasecounter@pmg{pfcasesnonumi},
        }
        \setlist[pfcasesnonum,2]{
            before=\def\pfcasecounter@pmg{pfcasesnonumii},
        }
        \setlist[pfcasesnonum,3]{
            before=\def\pfcasecounter@pmg{pfcasesnonumiii},
        }
        \newlist{pfcasesnumbered}{enumerate}{3}
        \setlist[pfcasesnumbered]{
          align=left,
          labelsep=!,
          itemindent=-1em,
          leftmargin=2em,
          labelindent=0pt,
          labelwidth=0pt
        }
        \setlist[pfcasesnumbered,1]{
            before=\def\pfcasecounter@pmg{pfcasesnumberedi},
          label={{\pmg@casefont{Case}}~\arabic*\protect\thiscase:~},
          ref={\arabic*},
        }
        \setlist[pfcasesnumbered,2]{
            before=\def\pfcasecounter@pmg{pfcasesnumberedii},
          label={{\pmg@casefont{Case}}~\arabic{pfcasesnumberedi}\alph*:\protect\thiscase.~},
          ref={\arabic{pfcasesnumberedi}\alph*},
        }
        \setlist[pfcasesnumbered,3]{
            before=\def\pfcasecounter@pmg{pfcasesnumberediii},
          label={{\pmg@casefont{Case}}~\arabic{pfcasesnumberedi}\alph{pfcasesnumberedii}.\roman*:\protect\thiscase.~},
          ref={\arabic{pfcasesnumberedi}\alph{pfcasesnumberedii}.\roman*},
        }
        \newenvironment{pfcases*}{
            \ProvideDocumentCommand{\case}{o}{
                \IfNoValueTF{##1}{
                    \def\thiscase{}%
                }{
                    \def\thiscase{~##1}%
                }
                \item  \ltx@ifpackageloaded{cleveref}{%
                \cref@constructprefix{pfcases}{\cref@result}%
                \protected@xdef\cref@currentlabel{[\pfcasecounter@pmg][][\cref@result]##1}}{}  \protected@edef\@currentlabel{##1}%
        }
        \begin{pfcasesnonum}
        }
        {\end{pfcasesnonum}}

        \newenvironment{pfcases}{
            \ProvideDocumentCommand{\case}{o}{
                \IfNoValueTF{##1}{
                    \def\thiscase{}%
                }{
                    \def\thiscase{~##1}%
                }
                \item \ltx@ifpackageloaded{cleveref}{%
                \cref@constructprefix{\pfcasecounter@pmg}{\cref@result}
                \protected@xdef\cref@currentlabel{[\pfcasecounter@pmg][][\cref@result] \csname the\pfcasecounter@pmg \endcsname}}{}%
        }
        \begin{pfcasesnumbered}}{\end{pfcasesnumbered}}
    \fi
}

\AtEndOfPackage{
\ifrecthy@nosubfun
    \@packinfo{Not loading subfun defs.}
\else
    \@packinfo{Loading subfun defs.}
    %DOCUMENT ME
    \NewDocumentCommand{\subfun}{o}{\prec\IfNoValueTF{#1}{}{_{#1}}}
    \NewDocumentCommand{\supfun}{o}{\succ\IfNoValueTF{#1}{}{_{#1}}}
    \NewDocumentCommand{\nsubfun}{o}{\nprec\IfNoValueTF{#1}{}{_{#1}}}
    \NewDocumentCommand{\nsupfun}{o}{\nsucc\IfNoValueTF{#1}{}{_{#1}}}
    \NewDocumentCommand{\subfuneq}{o}{\preceq\IfNoValueTF{#1}{}{_{#1}}}
    \NewDocumentCommand{\supfuneq}{o}{\succeq\IfNoValueTF{#1}{}{_{#1}}}
    \NewDocumentCommand{\nsubfuneq}{o}{\npreceq\IfNoValueTF{#1}{}{_{#1}}}
    \NewDocumentCommand{\nsupfuneq}{o}{\nsucceq\IfNoValueTF{#1}{}{_{#1}}}
    \NewDocumentCommand{\subfunneq}{o}{\precneq\IfNoValueTF{#1}{}{_{#1}}}
    \NewDocumentCommand{\supfunneq}{o}{\succneq\IfNoValueTF{#1}{}{_{#1}}}
\fi
}



% \newcommand*{\@recthy@reqscr}[1]{\mathscr{#1}}
\let\@recthy@reqscr=\mathscr
\DeclareOptionX{reqscr}{\edef\@recthy@reqscr{\expandafter\noexpand\csname #1 \endcsname}}


\AtEndOfPackage{
\ifrecthy@noreqhelper
    \@packinfo{Not loading requirement assist.}
\else
    \@packinfo{Loading requirement assist.}
    \newcommand*{\req@orig}[3][]{\ensuremath{\ifthenelse{\isempty{#1}}{\@recthy@reqscr{#2}_{#3}}{\@recthy@reqscr{#2}^{#1}_{#3}}}}
    \ifrecthy@hyperreqs
        \newcommand*{\req}[3][]{
        \@ifundefined{hyperref}{
            \req@orig[#1]{#2}{#3}
        }{
            \hyperref[\detokenize{req:#2@#1}]{\req@orig[#1]{#2}{#3}}
        }}
    \else
        \let\req=\req@orig
    \fi
    \WithSuffix\def\req*{\req@orig}
    % \newsavebox{\@recthy@reqbox}
    % \def\defreq#1#2\par{
    %   \begin{equation}\let\veqno\@@leqno%
    %       \tag*{#1}%
    %       \begin{lrbox}{\@recthy@reqbox}%
 %   \begin{minipage}{\textwidth}#2\end{minipage}%
 %   \end{lrbox}%
 %   \makebox[0pt]{\usebox{\@recthy@reqbox}}%
    %   \end{equation}}
    \newtagform{colon}{}{:}
    \newenvironment{requirement}[1]{
        \let\@origif@fleqn@pmg=\if@fleqn
        \let\@origiftagsleft@pmg=\iftagsleft@
        \@fleqntrue
        \setlength\@mathmargin{1.5cm}
        \tagsleft@true
        \usetagform{colon}
        % \let\maketag@@@orig@pmg=\maketag@@@
        % \def\maketag@@@#1{\hbox{\m@th\normalfont#1:}}
        \begin{equation}\tag{#1}
    }{
        \end{equation}
        \let\if@fleqn=\@origif@fleqn@pmg
        \let\iftagsleft@=\@origiftagsleft@pmg
        \usetagform{default}
        % \let\maketag@@@=\maketag@@@orig@pmg  
    }

    \newenvironment{require}[3][]{
        \begin{requirement}{\req*[#1]{#2}{#3}} \label{\detokenize{req:#2@#1}}
    }{
        \end{requirement}
    }
    \newcommand*{\refreq}[2][]{\ref{\detokenize{req:#2@#1}}}

\fi
}



\AtEndOfPackage{
\ifrecthy@nostructresets
    \@packinfo{Not loading r.e. set structs w/ containment.}
\else
    \@packinfo{Loading r.e. set structs w/ containment.}
\let\@orig@setminus=\setminus
\newcommand*{\promptdif}{\@orig@setminus_{\downarrow}}
\let\setbefore=\promptdif
\let\promptminus=\promptdif
\let\promptsetminus=\promptdif

\newcommand*{\StrcE}{\ensuremath{\mathscr{E}}}
\WithSuffix\def\StrcE*{\ensuremath{\mathscr{E}^{*}}}
\let\strucE\StrcE
\newcommand*{\StrcL}[1]{\mathscr{L}(#1)}
\newcommand*{\StrcStarL}[1]{\mathscr{L}^{*}(#1)}
\WithSuffix\def\StrcL*{\StrcStarL}
\newcommand*{\splitof}{\sqsubset}
\newcommand*{\splitby}{\sqsupset}
\newcommand*{\StrcR}{\ensuremath{\mathcal{R}}}
\newcommand*{\StrcD}{\ensuremath{\mathcal{D}}}


\fi
}

\AtEndOfPackage{
\ifrecthy@nohyphenation
    \@packinfo{No hyphenation loading.}
\else
\hyphenation{ra-tion-als ra-tion-al Harrington Slaman Cholak Knight Gerdes Lange}
\fi
}


\AtEndOfPackage{
\ifrecthy@mrref
    \@packinfo{MRref helper loading}
    \RequirePackage{hyperref}
    \def\recthy@checkMR MR#1#2#3 #4\relax%
      {\ifx#1M%
         \ifx#2R\recthy@MR{#3}\else\recthy@MR{#1#2#3}\fi
       \else
         \recthy@MR{#1#2#3}%
       \fi}
    \def\MR#1{\recthy@checkMR MR#1 \relax}
    \newcommand{\recthy@MR}[1]{\recthy@MRhref{#1}{MR #1}}
    % % \MRhref is called by the amsart/book/proc definition of \MR.
    \newcommand{\recthy@MRhref}[2]{\href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2}}
\else
    \@packinfo{MRref helper not loading}
\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.}
    \providecommand*{\eqdef}{\stackrel{\text{\tiny def}}{=}} %\newcommand*{\eqdef}{\ensuremath{=\limits_{\text{\tiny def}}}}
    \providecommand*{\iffdef}{\stackrel{\text{\tiny def}}{\iff}}
    \ifdefined\aut
    \else
        \DeclareMathOperator{\aut}{Aut}
    \fi
    \ifdefined\Ord
    \else
        \DeclareMathOperator{\Ord}{Ord}
    \fi

    \providecommand*{\meet}{\mathbin{\wedge}}
    \providecommand*{\join}{\mathbin{\vee}}
    \providecommand*{\Meet}{\mathop{\bigwedge}}
    \let\MnJoin=\Join
    \renewcommand*{\Join}{\mathop{\bigvee}}
    \recthy@strip{abs}
    \ifdefined\dom
    \else
        \DeclareMathOperator{\dom}{dom}
    \fi
    \ifdefined\rng
    \else
        \DeclareMathOperator{\rng}{rng}
    \fi
    \providecommand*{\restr}[1]{\mathpunct{\restriction_{#1}}}
    \providecommand*{\ordpair}[2]{\left( #1, #2 \right) }
    %%%%%%%%Function commands
    \providecommand*{\map}[2]{:#1\mapsto #2}
    \providecommand*{\functo}[3]{#1\map{#2}{#3}}
    \providecommand*{\compfunc}{\mathbin{\circ}}
    \ifdefined\compose
    \else
        \let\compose=\compfunc
    \fi
    \ifdefined\funcomp
    \else
        \let\funcomp=\compfunc
    \fi
    \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{reterms}{%
    \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{reaterms}{%
        \let\@recthy@CEA=\@recthy@REA
        }

\DeclareOptionX{ceterms}{%
    \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{ceaterms}{%
            \let\@recthy@REA=\@recthy@CEA
            }
% Set stuff



\NewDocumentCommand{\@recthy@set}{oG{}}{\left \{ #1 \ifthenelse{\isempty{#2}}{}{\middle | #2} \right \}}

% \def\@recthy@set#1{\def\@set@argi@pmg{#1}\@ifnextchar\bgroup\@setst@pmg\@setplain@pmg}
% \newcommand*{\@setst@pmg}[1]{\ifthenelse{\isempty{#1}}{\@setplain@pmg}{\left \{ \@set@argi@pmg \middle | #1\right \}}}
% \newcommand*{\@setplain@pmg}{\left \{ \@set@argi@pmg \right \}}
% \newcommand*{\@recthy@set}[2]{\ifthenelse{\isempty{#2}}{\left \{  #1 \right \}}{\left \{ #1 \middle | #2\right \}} }
% \DeclareOptionX{setminussym}[@recthy@defaultsetminusSYM]{\edef\@recthy@setminusSYM{\expandafter\noexpand\csname #1 \endcsname}}


\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@nin}{\notin}
\newcommand*{\@recthy@powset}[1]{\mathcal{P}\left(#1\right)}
\newcommand*{\@recthy@eset}{\emptyset}
% \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@setdiffSYM{-}
\newcommand*{\@recthy@setdiff}{\mathbin{\@recthy@setdiffSYM}}

\DeclareOptionX{setdiffsym}{\edef\@recthy@setdiffSYM{\expandafter\noexpand\csname #1 \endcsname}}





\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{setdiff}
    \let\crossOrig=\cross
    \def\cross{}
    \renewcommand*{\cross}{\mathbin{\times}}
    \let\CrossOrig=\Cross
    \def\Cross{}
    \renewcommand*{\Cross}{\mathop{\Pi}}
    \providecommand*{\symdiff}{\mathbin{\Delta}}
    \ifdefined\interior
    \else
        \DeclareMathOperator{\interior}{int}
    \fi
    \ifdefined\closure
    \else
        \DeclareMathOperator{\closure}{cl}
    \fi
\fi
}

\AtEndOfPackage{
\ifrecthy@noquants
    \@packinfo{No quants loading.}
\else
    \@packinfo{Quants loading.}
    \newcommand*{\existsuniq}{\exists !}
    \newcommand*{\nexistsuniq}{\nexists !}
    \WithSuffix\def\existsuniq(#1){\left(\existsuniq\, #1 \right)\!}
    \WithSuffix\def\nexistsuniq(#1){\left(\nexistsuniq\, #1 \right)\!}
    \WithSuffix\def\existsuniq[#1]{\left[\existsuniq\, #1 \right]\!}
    \WithSuffix\def\nexistsuniq[#1]{\left[\nexistsuniq\, #1 \right]\!}

    \newcommand*{\forallae}{\forall^{*}}
    \WithSuffix\def\forallae(#1){\left(\forallae\, #1\right)\!}
    \WithSuffix\def\forallae[#1]{\left[\forallae\, #1\right]\!}

    \providecommand*{\existsinf}{\exists^{\infty}}
    \WithSuffix\def\existsinf(#1){\left(\existsinf\, #1\right)\!}
    \WithSuffix\def\existsinf[#1]{\left[\existsinf\, #1\right]\!}

    \providecommand*{\nexistsinf}{\nexists^{\infty}}
    \WithSuffix\def\nexistsinf(#1){\left(\nexistsinf\, #1\right)\!}
    \WithSuffix\def\nexistsinf[#1]{\left[\nexistsinf\, #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\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}
    \WithSuffix\def\exists!{\existsuniq}




    \providecommand*{\True}{\top}
    \providecommand*{\False}{\bot}

    \providecommand*{\Land}{\mathop{\bigwedge}}
    \providecommand*{\Lor}{\mathop{\bigvee}}
    \providecommand*{\LLand}{\mathop{\bigwedge\mkern-15mu\bigwedge}}
    \providecommand*{\LLor}{\mathop{\bigvee\mkern-15mu\bigvee}}

    \providecommand*{\liff}{\ensuremath{\leftrightarrow}}
    \providecommand*{\limplies}{\ensuremath{\rightarrow}}
\fi
}

\AtEndOfPackage{
\ifrecthy@nospaces
    \@packinfo{No spaces loading.}
\else
    \@packinfo{Spaces loading.}

    \providecommand*{\bstrs}{2^{<\omega}}
    \providecommand*{\wstrs}{\omega^{<\omega}}

    \providecommand*{\cantor}{2^{\omega}}
    % \WithSuffix\def\cantor*{\left(2\union \diverge \right)^{\omega}}
    \providecommand*{\baire}{\omega^{\omega}}
    % \WithSuffix\def\baire*{\left(\omega \union \diverge \right)^{\omega}}
    \providecommand*{\Baire}{\mathcal{N}}
\fi
}


%Strings
\def\@recthy@concatSYM{\widehat{\;}}
\def\@recthy@EmptyStr{\mathopen{\@recthy@llangle}\mathclose{\@recthy@rrangle}}


\DeclareOptionX{emptystr}{\edef\@recthy@EmptyStr{\expandafter\noexpand\csname #1 \endcsname}}
\DeclareOptionX{concatsym}{\edef\@recthy@concatSYM{\expandafter\noexpand\csname #1 \endcsname}}


\AtEndOfPackage{
\ifrecthy@nostrings
    \@packinfo{No strings loading.}
\else
    \@packinfo{Strings loading.}
        \newcommand*{\closedn}[1]{{#1}^\blacktriangledown}
    \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}}
    \providecommand*{\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}^{-}}
    \providecommand*{\lh}[2][]{\@recthy@abs{#2}_{#1}} %% Gives length of a string
    \providecommand*{\incompat}{\mathrel{\mid}} %incompatible stringes FIX SPACING
    \providecommand*{\incomp}{\incompat}
    \providecommand*{\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}




%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^{*}}
    \providecommand*{\nsupset}{\not\supset}
    \providecommand*{\nsubset}{\not\subset}
    \WithSuffix\def\nsubset*{\nsubset^{*}}
    \WithSuffix\def\nsupset*{\nsupset^{*}}
    \WithSuffix\def\nsubseteq*{\nsubseteq^{*}}
    \WithSuffix\def\nsupseteq*{\nsupseteq^{*}}
    % \WithSuffix\def\subsetneq*{\subsetneq^{*}}
    % \WithSuffix\def\supsetneq*{\supsetneq^{*}}

    \newcommand*{\eq}{=}
    \WithSuffix\def\eq*{=^{*}}
    \newcommand*{\eqae}{=^{*}}
        \newcommand*{\neqae}{\neq^{*}}
    \WithSuffix\def\neq*{\neq^{*}}

    \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.}

\providecommand*{\wck}{\ensuremath{\omega^{ck}_1}}
  % \newcommand*{\ordtype}[1]{\ensuremath{\@recthy@abs{#1}_{\kleeneO}}}
    \newcommand*{\ordzero}{\ensuremath{0}}
  \def\kleeneOSYM{\mathcal{O}}
    \newcommand*{\kleeneO}{\let\@PMG@parenarg\@PMG@undefined\let\@PMG@braketarg\@PMG@undefined\@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*{\kleeneObelow}[2][]{\kleeneOSYM_{<#2\ifthenelse{\isempty{#1}}{}{, #1}}}
\let\kleeneOless\kleeneObelow

    \newcommand*{\kleeneOuniq}{\kleeneO*}
    \let\ordNotations=\kleeneO
    \let\uniqOrdNotations=\kleeneOuniq
    \NewDocumentCommand{\kleeneless}{o}{<_{\kleeneO\IfNoValueTF{#1}{}{,#1}}}
    \let\kleenel=\kleeneless
    \NewDocumentCommand{\kleeneleq}{o}{\leq_{\kleeneO\IfNoValueTF{#1}{}{,#1}}}
    \NewDocumentCommand{\kleenenless}{o}{\nless_{\kleeneO\IfNoValueTF{#1}{}{,#1}}}
    \let\kleenenl=\kleenenless
    \NewDocumentCommand{\kleenenleq}{o}{\nleq_{\kleeneO\IfNoValueTF{#1}{}{,#1}}}
    \NewDocumentCommand{\kleenegtr}{o}{>_{\kleeneO\IfNoValueTF{#1}{}{,#1}}}
    \let\kleeneg=\kleenegtr
    \NewDocumentCommand{\kleenegeq}{o}{\geq_{\kleeneO\IfNoValueTF{#1}{}{,#1}}}
    \NewDocumentCommand{\kleenengtr}{o}{\ngtr_{\kleeneO\IfNoValueTF{#1}{}{,#1}}}
    \let\kleeneng=\kleenengtr
    \NewDocumentCommand{\kleenengeq}{o}{\ngeq_{\kleeneO\IfNoValueTF{#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.}
    \providecommand*{\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@}{[][]}%
    % }
    \providecommand*{\frc}{\forces}
\fi
}


%%%%%%%%% Formula Classes

\newcommand*{\@recthy@CDelta}{\prescript{\mathcal{C}}{}{\Delta}}
\newcommand*{\@recthy@CSigma}{\prescript{\mathcal{C}}{}{\Sigma}}
\newcommand*{\@recthy@CPi}{\prescript{\mathcal{C}}{}{\Pi}}

\DeclareOptionX{cdeltasym}{\edef\@recthy@CDelta{\expandafter\noexpand\csname #1 \endcsname}}
\DeclareOptionX{csigmasym}{\edef\@recthy@CSigma{\expandafter\noexpand\csname #1 \endcsname}}
\DeclareOptionX{cpisym}{\edef\@recthy@CPi{\expandafter\noexpand\csname #1 \endcsname}}

% \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}}
    % \NewDocumentCommand{\hyplogic}{o}{\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}}
    \newcommand*{\Cpin}[1]{\CPi_{#1}}
    \WithSuffix\def\Cpin[#1]#2{\Cpin{#2}^{#1}}
    \newcommand*{\Csigman}[1]{\CSigma_{#1}}
    \WithSuffix\def\Csigman[#1]#2{\CSigma_{#2}^{#1}}

        \newcommand*{\CdeltaZeroN}[1]{\Cdeltan[0]{#1}}
    \newcommand*{\CdeltaZeroTwo}{\CdeltaZeroN{2}}
    \newcommand*{\CdeltaZeroThree}{\CdeltaZeroN{3}}
    \newcommand*{\CdeltaZeroOne}{\CdeltaZeroN{1}}
    \newcommand*{\CdeltaZeroZero}{\CdeltaZeroN{0}}
    \newcommand*{\CdeltaOneN}[1]{\Cdeltan[1]{#1}}
    \newcommand*{\CdeltaOneOne}{\CdeltaOneN{1}}
    \newcommand*{\CdeltaOneTwo}{\CdeltaOneN{2}}
    \newcommand*{\CdeltaOneThree}{\CdeltaOneN{3}}
        \newcommand*{\CpiZeroN}[1]{\Cpin[0]{#1}}
    \newcommand*{\CpiOneN}[1]{\Cpin[1]{#1}}
    \newcommand*{\CpiOneOne}{\CpiOneN{1}}
    \newcommand*{\CpiOneThree}{\CpiOneN{3}}
    \newcommand*{\CpiOneTwo}{\CpiOneN{2}}
    \newcommand*{\CpiZeroOne}{\CpiZeroN{1}}
    \newcommand*{\CpiZeroThree}{\CpiZeroN{3}}
    \newcommand*{\CpiZeroTwo}{\CpiZeroN{2}}
    \newcommand*{\CsigmaOneN}[1]{\Csigman[1]{#1}}
    \newcommand*{\CsigmaOneOne}{\CsigmaOneN{1}}
    \newcommand*{\CsigmaOneThree}{\CsigmaOneN{3}}
    \newcommand*{\CsigmaOneTwo}{\CsigmaOneN{2}}
    \newcommand*{\CsigmaZeroN}[1]{\Csigman[0]{#1}}
    \newcommand*{\CsigmaZeroOne}{\CsigmaZeroN{1}}
    \newcommand*{\CsigmaZeroThree}{\CsigmaZeroN{3}}
    \newcommand*{\CsigmaZeroTwo}{\CsigmaZeroN{2}}


    \WithSuffix\def\CsigmaOneN[#1]#2{\Csigma[1,#1]{#2}}
    \WithSuffix\def\CsigmaOneOne[#1]{\CsigmaOneN[#1]{1}}
    \WithSuffix\def\CsigmaOneThree[#1]{\CsigmaOneN[#1]{3}}
    \WithSuffix\def\CsigmaOneTwo[#1]{\CsigmaOneN[#1]{2}}
    \WithSuffix\def\CsigmaZeroN[#1]#2{\Csigma[0,#1]{#2}}
    \WithSuffix\def\CsigmaZeroOne[#1]{\CsigmaZeroN[#1]{1}}
    \WithSuffix\def\CsigmaZeroThree[#1]{\CsigmaZeroN[#1]{3}}
    \WithSuffix\def\CsigmaZeroTwo[#1]{\CsigmaZeroN[#1]{2}}
        \WithSuffix\def\CpiOneN[#1]#2{\Cpi[1,#1]{#2}}
    \WithSuffix\def\CpiOneOne[#1]{\CpiOneN[#1]{1}}
    \WithSuffix\def\CpiOneThree[#1]{\CpiOneN[#1]{3}}
    \WithSuffix\def\CpiOneTwo[#1]{\CpiOneN[#1]{2}}
    \WithSuffix\def\CpiZeroN[#1]#2{\Cpi[0,#1]{#2}}
    \WithSuffix\def\CpiZeroOne[#1]{\CpiZeroN[#1]{1}}
    \WithSuffix\def\CpiZeroThree[#1]{\CpiZeroN[#1]{3}}
    \WithSuffix\def\CpiZeroTwo[#1]{\CpiZeroN[#1]{2}}
        \WithSuffix\def\CdeltaOneN[#1]#2{\Cdelta[1,#1]{#2}}
    \WithSuffix\def\CdeltaOneOne[#1]{\CdeltaOneN[#1]{1}}
    \WithSuffix\def\CdeltaOneTwo[#1]{\CdeltaOneN[#1]{2}}
    \WithSuffix\def\CdeltaOneThree[#1]{\CdeltaOneN[#1]{3}}
        \WithSuffix\def\CdeltaZeroZero[#1]{\CdeltaZeroN[#1]{0}}
    \WithSuffix\def\CdeltaZeroN[#1]#2{\Cdelta[0,#1]{#2}}
        \WithSuffix\def\CdeltaZeroTwo[#1]{\CdeltaZeroN[#1]{2}}
        \WithSuffix\def\CdeltaZeroThree[#1]{\CdeltaZeroN[#1]{3}}
        \WithSuffix\def\CdeltaZeroOne[#1]{\CdeltaZeroN[#1]{1}}


    %%%ABREVIATIONS
    \newcommand*{\Cdeltaz}{\CdeltaN{0}}
    \newcommand*{\Cdeltazn}{\CdeltaZeroN}
    \newcommand*{\Cdeltazii}{\CdeltaZeroTwo}
    \newcommand*{\Cdeltazi}{\CdeltaZeroOne}
    \newcommand*{\Cdeltazz}{\CdeltaZeroZero}
    \newcommand*{\Cdeltaziii}{\CdeltaZeroThree}
    \newcommand*{\CdeltaIn}{\CdeltaOneN}
    \newcommand*{\CdeltaIi}{\CdeltaOneOne}
    \newcommand*{\Cdeltaoneone}{\CdeltaOneOne}
    \newcommand*{\CdeltaIii}{\CdeltaOneTwo}
    \newcommand*{\CdeltaIiii}{\CdeltaOneThree}
    \newcommand*{\Csigmazn}{\CsigmaZeroN}
    \newcommand*{\Csigmazi}{\CsigmaZeroOne}
    \newcommand*{\Csigmazii}{\CsigmaZeroTwo}
    \newcommand*{\Csigmaziii}{\CsigmaZeroThree}
    \newcommand*{\CsigmaIn}{\CsigmaOneN}
    \newcommand*{\CsigmaIi}{\CsigmaOneOne}
    \newcommand*{\CsigmaIii}{\CsigmaOneTwo}
    \newcommand*{\CsigmaIiii}{\CsigmaOneThree}
    \newcommand*{\Cpizn}{\CpiZeroN}
    \newcommand*{\Cpizi}{\CpiZeroOne}
    \newcommand*{\Cpizii}{\CpiZeroTwo}
    \newcommand*{\Cpiziii}{\CpiZeroThree}
    \newcommand*{\CpiIn}{\CpiOneN}
    \newcommand*{\CpiIi}{\CpiOneOne}
    \newcommand*{\CpiIii}{\CpiOneTwo}
    \newcommand*{\CpiIiii}{\CpiOneThree}

%%%BOLDFACE

    \newcommand*{\Deltan}[1]{\utilde{\symbf{\Delta}}_{#1}}
    \WithSuffix\def\Deltan[#1]#2{\utilde{\symbf{\Delta}}^{#1}_{#2}}
    % \WithSuffix\def\Deltan(#1)#2{\deltan{#2}\!\left(#1\right)}
    \newcommand*{\DeltaZeroN}[1]{\utilde{\symbf{\Delta}}^{0}_{#1}}
    \WithSuffix\def\DeltaZeroN[#1]#2{\utilde{\symbf{\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{\symbf{\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{\symbf{\Sigma}}_{#1}}
    \WithSuffix\def\Sigman[#1]#2{\utilde{\symbf{\Sigma}}^{#1}_{#2}}
    % \WithSuffix\def\Sigman(#1)#2{\sigman{#2}\!\left(#1\right)}
    \newcommand*{\SigmaZeroN}[1]{\utilde{\symbf{\Sigma}}^{0}_{#1}}
    \WithSuffix\def\SigmaZeroN[#1]#2{\utilde{\symbf{\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{\symbf{\Sigma}}^1_{#1}}
    \WithSuffix\def\SigmaOneN[#1]#2{\utilde{\symbf{\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{\symbf{\Pi}}_{#1}}
    \WithSuffix\def\Pin[#1]#2{\utilde{\symbf{\Pi}}^{#1}_{#2}}
    % \WithSuffix\def\Pin(#1)#2{\pin{#2}\!\left(#1\right)}
    \newcommand*{\PiZeroN}[1]{\utilde{\symbf{\Pi}}^0_{#1}}
    \WithSuffix\def\PiZeroN[#1]#2{\utilde{\symbf{\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{\symbf{\Pi}}^1_{#1}}
    \WithSuffix\def\PiOneN[#1]#2{\utilde{\symbf{\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
\DeclareOptionX{recfnlsym}[Phi]{\edef\recfnlSYM{\expandafter\noexpand\csname #1 \endcsname}}
\DeclareOptionX{recfsym}[phi]{\edef\recfSYM{\expandafter\noexpand\csname #1 \endcsname}}


%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} }}
\fi
}

\AtEndOfPackage{
\ifrecthy@nocomputations
    \@packinfo{No computations loading.}
\else
%%%%%%
    \newcommand*{\murec}[2]{\ensuremath{\mu#1\left( #2 \right) }}

    %\newcommand*{\brecfSYM}{\phi}
    \providecommand*{\recfSYM}{\phi}
    \providecommand*{\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)}%
    }}
    \NewDocumentCommand{\recf}{omod()}{
        \recfSYM_{#2\IfNoValueTF{#1}{}{, {#1}}}\IfNoValueTF{#3}{}{^{#3}}\IfNoValueTF{#4}{}{(#4)}
    }


    \newcommand*{\thetafnl}[4][]{\Theta_{#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*{\psifnl}[4][]{\Psi_{#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*{\phifnl}[4][]{\Phi_{#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*{\upsilonfnl}[4][]{\Upsilon_{#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{\simeq}}
    \newcommand*{\ncequiv}{\mathrel{\not\simeq}}
    \NewDocumentCommand{\conv}{o}{\mathpunct{\downarrow}_{#1}}
    \let\converge=\conv
    %\newcommand*{\convs}[1]{\ensuremath{\conv_{#1}}}
%   \NewDocumentCommand{\nconv}{o}{\mathpunct{\mkern-4mu{\arrownot\mkern 4mu \downarrow}_{#1}}}
    \NewDocumentCommand{\nconv}{o}{\mathpunct{\mkern-4mu{\smallsetminus\mkern 4mu \downarrow}_{#1}}}
    \newcommand*{\diverge}{\mathpunct{\uparrow}}
    % \newcommand*{\use}[2]{\mathscr{u}(#1\ifthenelse{\isempty{#2}}{}{,#2})}
    \newcommand*{\use}[1]{\mathop{\ltx@ifpackageloaded{unicode-math}{\symbffrak{u}}{\mathfrak{u}}}\!\left[{#1}\right]}

    % \NewDocumentCommand{\REset}{omd()}{
    % W_{#2\IfNoValueTF{#1}{}{, #1}}\IfNoValueTF{#3}{}{^{#3}}
    % }

    \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

\fi



\ifrecthy@nodegrees
    \@packinfo{No degrees loading.}
\else


    %%%%%%Turing Degrees
    \def\firsttokof@pmg#1{\first@pmg@rdmxs(#1)}
    \def\first@pmg@rdmxs(#1#2){#1}

    \providecommand*{\Tdegvar}[1]{\symbf{#1}}
    \providecommand*{\Tdegof}[1]{\utilde{#1}}
    \providecommand*{\Tdeg}[1]{\ifthenelse{
    %\equal{\detokenize{\Tzero}}{\futurelet\next@pmg\discard#1\@nil\expandafter\detokenize{\next@pmg}}
                                        \equal{\detokenize{\Tzero}}{\detokenize{#1}} \OR  
                                        \equal{\detokenize{\Tzero}}{\detokenize{#1}} \OR 
                                        \equal{\detokenize{\zeroj}}{\detokenize{#1}} \OR 
                                        \equal{\detokenize{\zerojj}}{\detokenize{#1}} \OR 
                                        \equal{\detokenize{\zerojjj}}{\detokenize{#1}} \OR 
                                        \equal{\string \zeron }{\expandafter\string \first@pmg@rdmxs(#1)}  
                                       }{\Tdegof{#1}}{\Tdegvar{#1}}}

    \providecommand*{\Tjump}[1]{#1'}
    \let\jump=\Tjump
    \providecommand*{\jumpn}[2]{#1^{(#2)}}
    \providecommand*{\jjump}[1]{#1''}
    % \newcommand*{\Tzerosym}{\MVZero}
    \newcommand*{\Tzerosym}{\mathbb{0}}
    \providecommand*{\Tzero}{{\Tzerosym}}
    \providecommand*{\zeron}[1]{{\Tzerosym}^{(#1)}}
    \providecommand*{\zeroj}{\jump{{\Tzerosym}}}
    \let\Tzeroj=\zeroj
    \providecommand*{\zerojj}{\jump{\jump{{\Tzerosym}}}}
    \providecommand*{\zerojjj}{\jump{\jump{\jump{{\Tzerosym}}}}}
    \let\Tzerojj=\zerojj
    \let\Tzerojjj=\zerojjj

    %%Misc Recursion theory stuff
    %turing equivalent
    \newcommand*{\@recthy@TSYM}{\symbf{T}}
    \providecommand*{\Tequiv}{\mathrel{\equiv_{\@recthy@TSYM}}}
    \providecommand*{\Teq}{\Tequiv}
    \providecommand*{\nTequiv}{\mathrel{\ncong_{\@recthy@TSYM}}}
    \providecommand*{\nTeq}{\nTequiv}
    %turing below

    \providecommand*{\Tlneq}{\lneq_{\@recthy@TSYM}}
    \providecommand*{\Tleq}{\leq_{\@recthy@TSYM}}
    \providecommand*{\Tgneq}{\gneq_{\@recthy@TSYM}}
    \providecommand*{\Tgeq}{\geq_{\@recthy@TSYM}}
    \providecommand*{\Tgtr}{>_{\@recthy@TSYM}}
    \providecommand*{\Tless}{<_{\@recthy@TSYM}}
    \providecommand*{\nTleq}{\nleq_{\@recthy@TSYM}}
    \providecommand*{\nTgeq}{\ngeq_{\@recthy@TSYM}}

    \providecommand*{\Tdegjoin}{\mathbin{\vee_{\@recthy@TSYM}}}
    \providecommand*{\Tdegmeet}{\mathbin{\wedge_{\@recthy@TSYM}}}
    \providecommand*{\Tmeet}{\Tdegmeet}
    \providecommand*{\Tsetjoin}{\mathbin{\oplus}}
    \providecommand*{\TsetJoin}{\mathop{\bigoplus}}
    \providecommand*{\Tplus}{\Tsetjoin}
    \providecommand*{\TPlus}{\TsetJoin}
    \providecommand*{\Tjoin}{\Tsetjoin}
    \providecommand*{\TJoin}{\TsetJoin}






    \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*{\ttnleq}{\nleq_{\@recthy@ttSYM}}
    \newcommand*{\ttngeq}{\ngeq_{\@recthy@ttSYM}}
\fi

}



% \ProcessOptions*
% \ProcessOptionsX<\@recthy@family>
\ProcessOptionsX