diff options
Diffstat (limited to 'Master/texmf-dist')
| -rw-r--r-- | Master/texmf-dist/doc/latex/rec-thy/README | 10 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/latex/rec-thy/rec-thy.pdf | bin | 225319 -> 226592 bytes | |||
| -rw-r--r-- | Master/texmf-dist/doc/latex/rec-thy/rec-thy.tex | 28 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/latex/rec-thy/rec-thy.sty | 330 |
4 files changed, 232 insertions, 136 deletions
diff --git a/Master/texmf-dist/doc/latex/rec-thy/README b/Master/texmf-dist/doc/latex/rec-thy/README index 12de6803c1b..677cb51aad4 100644 --- a/Master/texmf-dist/doc/latex/rec-thy/README +++ b/Master/texmf-dist/doc/latex/rec-thy/README @@ -1,8 +1,10 @@ -This directory contains the rec-thy package. This package provides a large number of macros to express standard pieces of notation in recursion theory aka computability theory. The file rec-thy.pdf (which can be generated from rec-thy.tex) provides a guide to usage and examples of almost all the macros. +This directory contains the rec-thy package. This package provides a large +number of macros to express standard pieces of notation in recursion theory +aka computability theory. The file rec-thy.pdf (which can be generated from +rec-thy.tex) provides a guide to usage and examples of almost all the macros. Comments, feedback and patches welcomes. -Author: Peter Gerdes -email: gerdes@invariant.org +Author: Peter Gerdes email: gerdes@invariant.org -10/14/2010
\ No newline at end of file +01/01/2011
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/rec-thy/rec-thy.pdf b/Master/texmf-dist/doc/latex/rec-thy/rec-thy.pdf Binary files differindex 7aa81b0ff08..27e0db319d8 100644 --- a/Master/texmf-dist/doc/latex/rec-thy/rec-thy.pdf +++ b/Master/texmf-dist/doc/latex/rec-thy/rec-thy.pdf diff --git a/Master/texmf-dist/doc/latex/rec-thy/rec-thy.tex b/Master/texmf-dist/doc/latex/rec-thy/rec-thy.tex index dd30364035e..1d5c511a798 100644 --- a/Master/texmf-dist/doc/latex/rec-thy/rec-thy.tex +++ b/Master/texmf-dist/doc/latex/rec-thy/rec-thy.tex @@ -40,7 +40,7 @@ \title{The rec-thy Package} \author{Peter M. Gerdes (gerdes@invariant.org)} -\date{2010-10-14: Version 1.0} +\date{2011-01-01: Version 1.2} \begin{document} @@ -72,7 +72,9 @@ A few general conventions are usually followed in the commands. Whenever an ope Objects that have a natural stagewise approximation generally admit an optional argument in brackets to specify a stage. For instance \( \verb=\REset[s]{e}= \) yields \( \REset[s]{e} \). An optional argument in parenthesis is used for relativization. For instance \( \verb=\REset(X){e}= \) produces \( \REset(X){e} \). A notable exception to this rule are the formula classes where square brackets are used to indicate an oracle to be placed in the superscript, e.g., \( \verb=\pizn[X]{2}= \) yields \( \pizn[X]{2} \), so as not to generate confusion with the alternative notion \( \pizn{2}(X) \). Also a lowercase first letter in a formula class indicates the lightface version while a capital first letter indicates the boldface version. Unless indicated otherwise all macros are to be used inside math mode. Indented commands indicate an alias for the command on the line above -\subsection{Main Commands} +\subsection{Computations} +To disable these commands pass the option \verb=nocomputations=. \\ + \begin{xtabular}{l | l | l}\toprule \verb=\murec{x}{f(x)>1}= & \( \murec{x}{f(x)>1} \) & Least \( x \) satisfying condition. \\ \midrule \verb=\recfnl{e}{Y}{x}= & \( \recfnl{e}{Y}{x} \) &\multirow{4}{*}{Computable functions/functionals} \\[6pt] @@ -96,7 +98,15 @@ Unless indicated otherwise all macros are to be used inside math mode. Indented \verb=\alphaREAop{\alpha}(\eset)= & \multirow{2}{*}{\( \alphaREAop{\alpha}(\eset) \)} &\multirow{2}{*}{\( \alpha \)-REA operator} \\[6pt] \tab \verb=\reaop{\alpha}(\eset)= & & \\[6pt] \verb=\alphaREAop[f]{\alpha}(\eset)= & \multirow{2}{*}{\( \alphaREAop[f]{\alpha}(\eset) \)} & \multirow{2}{*}{with particular witness to uniformity}\\[6pt] - \tab \verb=\reaop[f]{\alpha}(\eset)= & & \\ \midrule + \tab \verb=\reaop[f]{\alpha}(\eset)= & & \\ + \bottomrule + \end{xtabular} \\ + +\subsection{Degrees} +To disable these commands pass the option \verb=nodegrees=. \\ + + +\begin{xtabular}{l | l | l}\toprule \verb=\Tdeg{d}= & \( \Tdeg{d} \) & Turing degree \\ \midrule \verb=\Tjump{X}= & \multirow{2}{*}{\( \Tjump{X} \)} & \multirow{2}{*}{Turing jump} \\ \tab \verb=\jump{X}= & & \\ \midrule @@ -384,10 +394,18 @@ To disable these commands pass the option \verb=nosyntax=.\\ All syntax classes \verb=\logic{\omega_1}{\omega}= & \( \logic{\omega_1}{\omega} \) & Indicates the kind of infinitary logic\\ \bottomrule \end{xtabular} - + +\subsection{MRref} + +Finally to enable the mrref helper macros pass the option \verb=mrref=.\\ These macros normalize the formating of mathscinet references for supported bibliography styles and ensure the MR numbers link to the mathscinet page of the article. Unless you have a good reason (like journal formatting guidelines) there is no reason not to always pass this option. Note this option requires the hyperref package. - +\section{Release Notes} + +\begin{itemize} + \item[1.2] Fixed awful option processing bug preventing most options from being recognized and added mrref option. + \item[1.0] Initial public release +\end{itemize} diff --git a/Master/texmf-dist/tex/latex/rec-thy/rec-thy.sty b/Master/texmf-dist/tex/latex/rec-thy/rec-thy.sty index 414ba560a33..9c8b1e5bce1 100644 --- a/Master/texmf-dist/tex/latex/rec-thy/rec-thy.sty +++ b/Master/texmf-dist/tex/latex/rec-thy/rec-thy.sty @@ -3,8 +3,12 @@ \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 +\ProvidesPackage{\@curpack} [2011/01/01 v1.2 Provides commands for writing up recursion theory papers] %file name is package name +% Release Notes +% Version 1.2 +% Added mrref option +% Fixed horrific option processing bug \RequirePackage{suffix} \RequirePackage{ifmtarg} @@ -21,8 +25,49 @@ \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... + +\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 + +\DeclareOption{nohyphenation}{\recthy@nohyphenationtrue} +\DeclareOption{mrref}{\recthy@mrreftrue} +\DeclareOption{nomath}{\recthy@nomathtrue} +\DeclareOption{nodelim}{\recthy@nodelimtrue} +\DeclareOption{nonames}{\recthy@nonamestrue} +\DeclareOption{nosets}{\recthy@nosetstrue} +\DeclareOption{noquants}{\recthy@noquantstrue} +\DeclareOption{nospaces}{\recthy@nospacestrue} +\DeclareOption{nostrings}{\recthy@nostringstrue} +\DeclareOption{notrees}{\recthy@notreestrue} +\DeclareOption{nopair}{\recthy@nopairtrue} +\DeclareOption{nosetrels}{\recthy@nosetrelstrue} +\DeclareOption{noordinalnotations}{\recthy@noordinalnotationstrue} +\DeclareOption{nosyntax}{\recthy@nosyntaxtrue} +\DeclareOption{nodegclasses}{\recthy@nodegclassestrue} +\DeclareOption{noforcing}{\recthy@noforcingtrue} +\DeclareOption{nodegrees}{\recthy@nodegreestrue} +\DeclareOption{nocomputations}{\recthy@nocomputationstrue} + +\DeclareOption{degjoin}{\def\Tjoin{\Tdegjoin}} + \AtEndOfPackage{ \ifrecthy@nohyphenation \@packinfo{No hyphenation loading.} @@ -31,6 +76,26 @@ \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{ @@ -137,25 +202,25 @@ \fi } -\DeclareOptionX<\@recthy@family>{re}{% +\DeclareOption{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<\@recthy@family>{rea}{% + \DeclareOption{reaterms}{% \let\@recthy@CEA=\@recthy@REA } -\DeclareOptionX<\@recthy@family>{ce}{% +\DeclareOption{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<\@recthy@family>{cea}{% +\DeclareOption{ceaterms}{% \let\@recthy@REA=\@recthy@CEA } % Set stuff @@ -179,9 +244,9 @@ \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} +\DeclareOption{setminussym}{\def\@recthy@setminusSYM{#1}} +\DeclareOption{setcmpminussym}{\def\@recthy@setminusSYM{#1}} +\DeclareOption{minussetcmp}{\let\@recthy@setcmp=\@recthy@setminuscmp} \newcommand*{\@recthy@setminus}{\mathbin{\@recthy@setminusSYM}} @@ -278,7 +343,7 @@ %Strings -\newcommand*{\@recthy@EmptyStr}{\str{}} +\newcommand*{\@recthy@EmptyStr}{\lambda} \newcommand*{\@recthy@concatSYM}{\hat{}} \DeclareOptionX<\@recthy@family>{emptystr}[]{\def\@recthy@EmptyStr{#1}} \DeclareOptionX<\@recthy@family>{concat}[]{\def\@recthy@concatSYM{#1}} @@ -334,117 +399,6 @@ % \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}} @@ -574,13 +528,10 @@ _{#1} \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}} +\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 @@ -916,8 +867,133 @@ _{#1} \fi } + +% \ProcessOptions* \ProcessOptionsX<\@recthy@family> +\ifrecthy@nocomputations + \@packinfo{No computations loading.} +\else +%%%%%% + \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 + +\fi + + + +\ifrecthy@nodegrees + \@packinfo{No degrees loading.} +\else + + + %%%%%%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} + + + + + + + \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}} +\fi + + + |