Double Stone algebras

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

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\begin{document}
\textbf{\Large Double Stone algebras}
\quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Double_Stone_algebras}{edit}

\abbreviation{DblStAlg}
\begin{definition}
A \emph{double Stone algebra} is a structure $\mathbf{L}=\langle L,\vee ,0,\wedge ,1,^*\rangle $ such that


$\langle L,\vee,0,\wedge,1,^*\rangle $ is a \href{Stone_algebras.pdf}{Stone algebras}


$\langle L,\wedge,1,\vee,0,^*\rangle $ is a \href{Stone_algebras.pdf}{Stone algebras}

\end{definition}
\begin{morphisms}
Let $\mathbf{L}$ and $\mathbf{M}$ be double Stone algebras. A morphism from $\mathbf{L}$ to $\mathbf{M}$ is a function $h:L\rightarrow M$ that is a
homomorphism: 

$h(x\vee y)=h(x)\vee h(y)$, $h(x\wedge y)=h(x)\wedge h(y)$, $h(0)=0 $, $h(1)=1$, $h(x^*)=h(x)^*$

\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 & \\\hline
Quasiequational theory & \\\hline
First-order theory & \\\hline
Congruence distributive & yes\\\hline
Congruence modular & yes\\\hline
Congruence n-permutable & \\\hline
Congruence regular & \\\hline
Congruence uniform & \\\hline
Congruence extension property & yes\\\hline
Definable principal congruences & \\\hline
Equationally def. pr. cong. & \\\hline
Amalgamation property & \\\hline
Strong amalgamation property & \\\hline
Epimorphisms are surjective & \\\hline
Locally finite & \\\hline
Residual size & \\\hline
\end{tabular}
\end{properties}
\end{table}
\begin{finite_members} $f(n)=$ number of members of size $n$.

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\begin{subclasses}\ 

\href{Boolean_algebras.pdf}{Boolean algebras} 

\end{subclasses}
\begin{superclasses}\ 

\href{Stone_algebras.pdf}{Stone algebras} 

\end{superclasses}

\begin{thebibliography}{10}

\bibitem{Ln19xx}

\end{thebibliography}

\end{document}
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