History of Join-semidistributive lattices

 
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 \begin{document}
 \textbf{\Large Join-semidistributive lattices}
 \quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Join-semidistributive_lattices}{edit}
 
 \abbreviation{JsdLat}
 \begin{definition}
 A \emph{join-semidistributive lattice} is a lattice $\mathbf{L}=\langle L,\vee
 ,\wedge \rangle$ that satisfies
 
 the join-semidistributive law SD$_{\vee}$:  $x\vee y=x\vee z\implies x\vee y=x\vee(y\wedge z)$
 \end{definition}
 
 \begin{morphisms}
 Let $\mathbf{L}$ and $\mathbf{M}$ be join-semidistributive lattices. A morphism from $\mathbf{L}$ to $\mathbf{M}$ is a function 
 $h:L\rightarrow M$ that is a homomorphism: 
 
 $h(x\vee y)=h(x)\vee h(y)$, $h(x\wedge y)=h(x)\wedge h(y)$
 \end{morphisms}
 
 \begin{basic_results}
 \end{basic_results}
 \begin{examples}
 \begin{example}
 $D[d]=\langle D\cup\{d'\},\vee ,\wedge\rangle$, where $D$ is any distributive lattice and $d$ is an element in it that
 is split into two elements $d,d'$ using Alan Day's doubling construction.
 \end{example}
 \end{examples}
 \begin{table}[h]
 \begin{properties} (\href{http://math.chapman.edu/cgi-bin/structures?Properties}{description})
 
 \begin{tabular}{|ll|}\hline
 Classtype & quasivariety\\\hline
 Equational theory & \\\hline
 Quasiequational theory & \\\hline
 First-order theory & undecidable\\\hline
 Congruence distributive & yes\\\hline
 Congruence modular & yes\\\hline
 Congruence n-permutable & no\\\hline
 Congruence regular & no\\\hline
 Congruence uniform & no\\\hline
 Congruence extension property & \\\hline
 Definable principal congruences & \\\hline
 Equationally def. pr. cong. & \\\hline
 Amalgamation property & no\\\hline
 Strong amalgamation property & no\\\hline
 Epimorphisms are surjective & \\\hline
 Locally finite & no\\\hline
 Residual size & unbounded\\\hline
 \end{tabular}
 \end{properties}
 \end{table}
 \begin{finite_members} $f(n)=$ number of members of size $n$.
 
 $\begin{array}{lr}
 f(1)= &1\\
 f(2)= &1\\
 f(3)= &1\\
 f(4)= &\\
 f(5)= &\\
 f(6)= &\\
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 \end{array}$
 \end{finite_members}
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 \begin{subclasses}\ 
 
 \href{Semidistributive_lattices.pdf}{Semidistributive lattices} 
 
 \end{subclasses}
 \begin{superclasses}\ 
 
 \href{Lattices.pdf}{Lattices} 
 
 \end{superclasses}
 
 \begin{thebibliography}{10}
 
 \bibitem{Ln19xx}
 
 \end{thebibliography}
 
 \end{document}
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