Mathematical Structures: Generalized Boolean algebras

Generalized Boolean algebras

http://mathcs.chapman.edu/structuresold/files/Generalized_Boolean_algebras.pdf
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\newtheorem*{morphisms}{Morphisms}
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\begin{document}
\textbf{\Large Generalized Boolean algebras}

\abbreviation{GBA}

\begin{definition}
A \emph{generalized Boolean algebra} is a \href{Brouwerian_algebras.pdf}{Brouwerian algebras}
$\mathbf{A}=\langle A, \vee, \wedge, 1, \rightarrow\rangle$ such that

$x\vee y=(x\rightarrow y)\rightarrow y$
\end{definition}

\begin{morphisms}
Let $\mathbf{A}$ and $\mathbf{B}$ be generalized Boolean algebras. A
morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$
that is a homomorphism:

$h(x\vee y)=h(x)\vee h(y)$, $h(x\wedge y)=h(x)\wedge h(y)\ \mbox{and} h(1)=1$, $h(x\rightarrow y)=h(x)\rightarrow h(y)$
\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 & decidable\\\hline
First-order theory & decidable\\\hline
Locally finite & yes\\\hline
Residual size & $2$\\\hline
Congruence distributive & yes\\\hline
Congruence modular & yes\\\hline
Congruence n-permutable & yes, $n=2$\\\hline
Congruence regular & yes\\\hline
Congruence e-regular & yes, $e=1$\\\hline
Congruence uniform & yes\\\hline
Congruence extension property & yes\\\hline
Definable principal congruences & yes\\\hline
Equationally def. pr. cong. & yes\\\hline
Amalgamation property & yes\\\hline
Strong amalgamation property & yes\\\hline
Epimorphisms are surjective & yes\\\hline
\end{tabular}
\end{properties}
\end{table}

\begin{finite_members} $f(n)=$ number of members of size $n$.

$\begin{array}{lr} f(1)= &1\\ f(2)= &1\\ f(3)= &0\\ f(4)= &1\\ f(5)= &0\\ f(6)= &0\\ \end{array}$
\end{finite_members}

\hyperbaseurl{http://math.chapman.edu/structures/files/}
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\begin{subclasses}\

\href{Boolean_algebras.pdf}{Boolean algebras}

\end{subclasses}

\begin{superclasses}\

\href{Brouwerian_algebras.pdf}{Brouwerian algebras}

\href{Wajsberg_hoops.pdf}{Wajsberg hoops}

\end{superclasses}

\begin{thebibliography}{10}

\bibitem{Ln19xx}

\end{thebibliography}

\end{document}
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