Vaught's testVaughtsTest2002-08-29 21:42:152002-09-04 10:26:32Theoremmodel theorylogic% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
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% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
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%\usepackage{psfrag}
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%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
\newenvironment{proof}[1][Proof]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
\newenvironment{definition}[1][Definition]{\begin{trivlist}
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\newenvironment{example}[1][Example]{\begin{trivlist}
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\newenvironment{remark}[1][Remark]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}Let $L$ be a first order language, and let $S$ be a set of $L$-sentences with no finite models which is $\kappa$-categorical for some $\kappa \geq |L|$. Then $S$ is \PMlinkname{complete}{FirstOrderTheories}.