\newcommand{\defn}{\underline}
\renewcommand{\qed}{\hfill\ensuremath{\Box}}
\providecommand{\Dashv}{\mathrel{\text{\reflectbox{$\vDash$}}}}

\providecommand{\eq}{\operatorname{eq}}
\providecommand{\stp}{\operatorname{stp}}
\providecommand{\mult}{\operatorname{mult}}
\newcommand{\Deq}{D^{\eq}}
\newcommand{\MM}{\mathbb{M}} %monster model
\newcommand{\MMeq}{\MM^{\eq}}

\newcommand{\tuple}[1]{\overline{#1}}
\newcommand{\atup}{\tuple{a}}
\newcommand{\btup}{\tuple{b}}
\newcommand{\ctup}{\tuple{c}}
\newcommand{\dtup}{\tuple{d}}
\newcommand{\wtup}{\tuple{w}}
\newcommand{\xtup}{\tuple{x}}
\newcommand{\ytup}{\tuple{y}}
\newcommand{\ztup}{\tuple{z}}

\providecommand{\stp}{\operatorname{stp}}
\providecommand{\tp}{\operatorname{tp}}
\providecommand{\dcl}{\operatorname{dcl}}
\providecommand{\acl}{\operatorname{acl}}
\providecommand{\cl}{\operatorname{cl}}
\providecommand{\dom}{\operatorname{dom}}
\providecommand{\Stab}{\operatorname{Stab}}
\providecommand{\Aut}{\operatorname{Aut}}
\providecommand{\Cb}{\operatorname{Cb}}
\providecommand{\Th}{\operatorname{Th}}

\providecommand{\N}{\mathbb{N}}
\providecommand{\Z}{\mathbb{Z}}

\newcommand{\acleq}{\operatorname{acl}^{\operatorname{eq}}}
\newcommand{\dcleq}{\operatorname{dcl}^{\operatorname{eq}}}

\providecommand{\PP}{\mathbb{P}}
\providecommand{\Pset}{\mathcal{P}}

\providecommand{\pp}{\mathfrak{p}}
\providecommand{\qq}{\mathfrak{q}}
\providecommand{\rr}{\mathfrak{r}}

\providecommand{\CC}{\mathcal{C}}
\providecommand{\BB}{\mathcal{B}}

\providecommand{\sg}{\sigma}

\providecommand{\aCb}{\overline{\Cb}}

\providecommand{\infix}[1]{\;\textrm{#1}\;}

\providecommand{\Wedge}{\bigwedge}
\providecommand{\Vee}{\bigvee}

\renewcommand{\restriction}{\mathord{\upharpoonright}}

% corner quotes; adapted from a definition due to Sam Buss, taken from
% http://www.logicmatters.net/latex-for-logicians/symbols/corner-quotes-for-godel-numbers/
\newbox\gnBoxA
\newdimen\gnCornerHgt
\setbox\gnBoxA=\hbox{$\ulcorner$}
\global\gnCornerHgt=\ht\gnBoxA
\newdimen\gnArgHgt
\def\code #1{%
\setbox\gnBoxA=\hbox{$#1$}%
\gnArgHgt=\ht\gnBoxA%
\ifnum     \gnArgHgt<\gnCornerHgt \gnArgHgt=0pt%
\else \advance \gnArgHgt by -\gnCornerHgt%
\fi \raise\gnArgHgt\hbox{$\ulcorner$} \box\gnBoxA \, %
\raise\gnArgHgt\hbox{$\urcorner$}}

% Rahim's nonforking symbol (I don't know where got it from)
\def\Ind#1#2{#1\setbox0=\hbox{$#1x$}\kern\wd0\hbox to 0pt{\hss$#1\mid$\hss}
\lower.9\ht0\hbox to 0pt{\hss$#1\smile$\hss}\kern\wd0}
\def\ind{\mathop{\mathpalette\Ind{}}}
\def\notind#1#2{#1\setbox0=\hbox{$#1x$}\kern\wd0\hbox to 0pt{\mathchardef
\nn=12854\hss$#1\nn$\kern1.4\wd0\hss}\hbox to
0pt{\hss$#1\mid$\hss}\lower.9\ht0 \hbox to
0pt{\hss$#1\smile$\hss}\kern\wd0}
\def\nind{\mathop{\mathpalette\notind{}}}

\bibliographystyle{alpha}
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{fact}[theorem]{Fact}
\newtheorem*{fact*}{Fact}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{claim}[theorem]{Claim}
\newtheorem*{claim*}{Claim}
\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem*{definition*}{Definition}
\newtheorem{notation}[theorem]{Notation}
\newtheorem*{notation*}{Notation}
\theoremstyle{remark}
\newtheorem{remark}[theorem]{Remark}
\newtheorem*{remark*}{Remark}
\newtheorem{example}[theorem]{Example}
\newtheorem*{example*}{Example}
\newtheorem{note}[theorem]{Note}
\newtheorem*{note*}{Note}
\newtheorem{question}[theorem]{Question}

\newtheorem*{question*}{Question}
\newtheorem*{exercise*}{Exercise}
\newtheorem*{recall*}{Recall}
\newtheorem*{historicalremark*}{Historical Remark}
\newtheorem*{convention*}{Convention}

