| 15083 |      1 | \documentclass[11pt,a4paper]{article}
 | 
|  |      2 | \usepackage{graphicx}
 | 
|  |      3 | \usepackage{isabelle,amssymb,isabellesym}
 | 
|  |      4 | \usepackage{pdfsetup}\urlstyle{rm}
 | 
|  |      5 | 
 | 
|  |      6 | %table of contents is too crowded!
 | 
|  |      7 | \usepackage{tocloft}
 | 
|  |      8 | \addtolength\cftsubsecnumwidth {0.5em}
 | 
|  |      9 | \addtolength\cftsubsubsecnumwidth {1.0em}
 | 
|  |     10 | 
 | 
|  |     11 | \begin{document}
 | 
|  |     12 | 
 | 
|  |     13 | \title{Equivalents of the Axiom of Choice}
 | 
|  |     14 | \author{Krzysztof Gr\c{a}bczewski}
 | 
|  |     15 | \maketitle
 | 
|  |     16 | 
 | 
|  |     17 | \begin{abstract}
 | 
|  |     18 |   This development~\cite{paulson-gr} proves the equivalence of seven
 | 
|  |     19 |   formulations of the well-ordering theorem and twenty formulations of the
 | 
|  |     20 |   axiom of choice. It formalizes the first two chapters of the monograph
 | 
|  |     21 |   \emph{Equivalents of the Axiom of Choice} by Rubin and
 | 
|  |     22 |   Rubin~\cite{rubin&rubin}. Some of this mmaterial involves extremely complex
 | 
|  |     23 |   techniques.
 | 
|  |     24 | \end{abstract}
 | 
|  |     25 | 
 | 
|  |     26 | \tableofcontents
 | 
|  |     27 | 
 | 
|  |     28 | \begin{center}
 | 
| 17159 |     29 |   \includegraphics[width=\textwidth]{session_graph}
 | 
| 15083 |     30 | \end{center}
 | 
|  |     31 | 
 | 
|  |     32 | \newpage
 | 
|  |     33 | 
 | 
|  |     34 | \parindent 0pt\parskip 0.5ex
 | 
|  |     35 | 
 | 
|  |     36 | \input{session}
 | 
|  |     37 | 
 | 
|  |     38 | \bibliographystyle{plain}
 | 
|  |     39 | \bibliography{root}
 | 
|  |     40 | 
 | 
|  |     41 | \end{document}
 |