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\Large Name of class \quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Template}{edit} % Note: replace "Template" with Name_of_class in previous line |
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\Large Monadic algebras \quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Monadic_algebras}{edit} |
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\abbreviation{Abbr} |
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\abbreviation{MonA} |
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A ... is a structure $\mathbf{A}=\langle A,...\rangle$ of type $\langle ...\rangle$ such that |
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A monadic algebra is a structure $\mathbf{A}=\langle A, \vee, 0, \wedge, 1, \neg, f\rangle$ of type $\langle 2, 0, 2, 0, 1, 1\rangle$ such that |
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$\langle A,...\rangle$ is a \href{Name_of_class.pdf}{name of class} |
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$\langle A, \vee, 0, \wedge, 1, \neg\rangle$ is a \href{Boolean_algebras.pdf}{Boolean algebra} |
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$op_1$ is (name of property): $axiom_1$ |
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$f$ is a unary closure operator: $f(x\vee y)=f(x)\vee f(y)$, $f(0)=0$, $x\le f(x)=f(f(x))$ |
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$op_2$ is ...: $...$ |
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$f$ is self conjugated: $f(x)\wedge y=0\iff x\wedge f(y)=0$ |
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Let $\mathbf{A}$ and $\mathbf{B}$ be ... . A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism: $h(x ... y)=h(x) ... h(y)$ |
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Let $\mathbf{A}$ and $\mathbf{B}$ be monodic algebras. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism: $h(x \vee y)=h(x) \vee h(y)$, $h(\neg x)=\neg h(x)$, $h(f(x))=f(h(x))$. |
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Classtype & (value, see description) \cite{Ln19xx} \\\hline Equational theory & \\\hline |
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Classtype & variety \\\hline Equational theory & decidable\\\hline |
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Congruence distributive & \\\hline Congruence modular & \\\hline Congruence $n$-permutable & \\\hline Congruence regular & \\\hline Congruence uniform & \\\hline Congruence extension property & \\\hline Definable principal congruences & \\\hline Equationally def. pr. cong. & \\\hline Amalgamation property & \\\hline |
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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 & yes\\\hline Equationally def. pr. cong. & yes\\\hline Amalgamation property & yes\\\hline |
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f(2)= &\\ |
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f(2)= &1\\ |
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\href{....pdf}{...} supervariety |
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\href{Boolean_algebras.pdf}{Boolean algebras} reduced type |
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\href{....pdf}{...} subreduct |
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\href{Closure_algebras.pdf}{Closure algebras} |
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\bibitem{Ln19xx} |
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\bibitem{Lastname19xx} |
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