%\documentclass[12pt]{amsbook} %\documentclass[12pt]{amsart} %\usepackage[notcite]{showkeys} %\usepackage{verbatim} \usepackage{amssymb,latexsym,amsmath,amsthm} %\documentclass{ams} %\usepackage{layout} %\usepackage{epic,eepic} % Needed for some of the pictures Kemal drew for me %\usepackage{epic} % Needed for \dashline, which is used below %\usepackage{graphpap} %\usepackage{color} %\usepackage{fancyheadings} %\pagestyle{fancy} %\usepackage{setspace} %\includeonly{} %\lheadInductive Definability on Arbitrary Sets[]{} %\chead[]{} %\rhead[]{} %\lfoot[Book-Combined.tex\ \today]{Book-Combined.tex} %\rfoot[]{} %\cfoot[\thepage]{\thepage} %\author{Wayne Richter} %\address{Department of Mathematics\\ %University of Minnesota\\ %Minneapolis, MN 55455} %\email{richterDeltamath.umn.edu} %................... New theorems \newtheorem{theorem}{Theorem}[section] \newtheorem{proposition}[theorem]{Proposition} \newtheorem{examples}[theorem]{Examples} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{axiom}[theorem]{Axiom} %........These will be typeset in Roman \bibliographystyle{asl} \theoremstyle{definition} \newtheorem*{exercises}{\textbf{Exercises}} \newtheorem{exercise}[theorem]{Exercise} \newtheorem{discussion}[theorem]{\textit{Discussion}} \newtheorem{definition}[theorem]{Definition} \newtheorem{fact}[theorem]{Fact} %\newtheorem{remark}[theorem]{Remark} \newtheorem*{hint}{\textit{Hint}} \newtheorem*{caution}{\textit{Caution}} \newtheorem{note}[theorem]{\textit{Note}} \newtheorem{example}[theorem]{Example} \bibliographystyle{asl} \theoremstyle{definition} \newtheorem{openproblem}[theorem]{Open Problem} \newtheorem{summary}[theorem]{Summary} \newtheorem{goal}[theorem]{\bf GOAL} \newtheorem{question}[theorem]{\textit{Question}} \newtheorem{questions}[theorem]{\textit{Questions}} \newtheorem{remark}[theorem]{Remark} \newtheorem*{claim}{\textit{Claim}} \newtheorem*{proofofclaim}{\textit{Proof of Claim}} \newtheorem*{case}{\textit{Case}} \newtheorem*{notation}{\textit{Notation}} \newcommand{\maps}[3]{#1\colon#2\longrightarrow#3} \newcommand{\ran}{\textrm{ran}} \newcommand{\dom}{\textrm{dom}}