Boolean algebras with operators

http://mathcs.chapman.edu/structuresold/files/Boolean_algebras_with_operators.pdf

%%run pdflatex

%

\documentclass[12pt]{amsart}
\usepackage[pdfpagemode=Fullscreen,pdfstartview=FitBH]{hyperref}
\parindent=0pt
\parskip=5pt
\addtolength{\oddsidemargin}{-.5in}
\addtolength{\evensidemargin}{-.5in}
\addtolength{\textwidth}{1in}
\theoremstyle{definition}
\newtheorem{definition}{Definition}
\newtheorem*{morphisms}{Morphisms}
\newtheorem*{basic_results}{Basic Results}
\newtheorem*{examples}{Examples}
\newtheorem{example}{}
\newtheorem*{properties}{Properties}
\newtheorem*{finite_members}{Finite Members}
\newtheorem*{subclasses}{Subclasses}
\newtheorem*{superclasses}{Superclasses}
\newcommand{\abbreviation}[1]{\textbf{Abbreviation: #1}}
\pagestyle{myheadings}\thispagestyle{myheadings}
\markboth{\today}{math.chapman.edu/structures}

\begin{document}
\textbf{\Large Boolean algebras with operators}
\quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Boolean_algebras_with_operators}{edit}

\abbreviation{BAO}
\begin{definition}
A \emph{Boolean algebra with operators} is a structure $\mathbf{A}=\langle A,\vee,0,
\wedge,1,\neg,f_i\ (i\inI)\rangle$ such that


$\langle A,\vee,0,\wedge,1,\neg\rangle$ is a Boolean algebra


$f_i$ is \emph{join-preserving} in each argument:  
$f_i(\ldots,x\vee y,\ldots)=f_i(\ldots,x,\ldots)\vee f_i(\ldots,y,\ldots)$


$f_i$ is \emph{normal} in each argument:  $f_i(\ldots,0,\ldots)=0$

\end{definition}
\begin{morphisms}
Let $\mathbf{A}$ and $\mathbf{B}$ be Boolean algebras with operators of the same signature. 
A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a Boolean homomorphism and preserves all the operators:

$h(f_i(x_0,\ldots,x_{n-1}))=f_i(h(x_0),\ldots,h(x_{n-1}))$
\end{morphisms}
\begin{basic_results}
\end{basic_results}
\begin{examples}
\begin{example}
\end{example}
\end{examples}

\begin{table}[h]
\begin{properties} (\href{http://math.chapman.edu/cgi-bin/structures?Properties}{description})

\begin{tabular}{|ll|}\hline
Classtype & variety\\\hline
Equational theory & decidable\\\hline
Quasiequational theory & \\\hline
First-order theory & undecidable\\\hline
Locally finite & no\\\hline
Residual size & unbounded\\\hline
Congruence distributive & yes\\\hline
Congruence modular & yes\\\hline
Congruence n-permutable & yes, $n=2$\\\hline
Congruence regular & yes\\\hline
Congruence uniform & yes\\\hline
Congruence extension property & yes\\\hline
Definable principal congruences & no\\\hline
Equationally def. pr. cong. & no\\\hline
Amalgamation property & yes\\\hline
Strong amalgamation property & yes\\\hline
Epimorphisms are surjective & yes\\\hline
\end{tabular}
\end{properties}
\end{table}
\hyperbaseurl{http://math.chapman.edu/structures/files/}
\parskip0pt
\begin{subclasses}\ 

\href{Modal_algebras.pdf}{Modal algebras} 

\href{Boolean_monoids.pdf}{Boolean monoids} 

\end{subclasses}
\begin{superclasses}\ 

\href{Boolean_algebras.pdf}{Boolean algebras} 

\end{superclasses}

\begin{thebibliography}{10}

\bibitem{Ln19xx}

\end{thebibliography}

\end{document}
%