Complete distributive lattices

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

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\begin{document}
\textbf{\Large Complete distributive lattices}
\quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Complete distributive lattices}{edit}

\abbreviation{CDLat}

\begin{definition}
A \emph{complete distributive lattice} is a \href{Complete_lattices.pdf}{complete lattice} $\mathbf{A}=\langle A,\bigvee,\bigwedge\rangle$ such that

$\vee$ distributes over $\wedge$:  $x\vee (y\wedge z)=(x\vee y)\wedge(x\vee z)$

Remark: 
Click on the 'Edit text of this page' link at the bottom to add some information about complete distributive lattices

It is not unusual to give several (equivalent) definitions. Ideally, one of the definitions would give an irredundant axiomatization that does not refer to other classes.
\end{definition}

\begin{morphisms}
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: 
$h(x ... y)=h(x) ... h(y)$
\end{morphisms}

\begin{definition}
An \emph{...} is a structure $\mathbf{A}=\langle A,...\rangle$ of type $\langle
...\rangle$ such that

$...$ is ...:  $axiom$
  
$...$ is ...:  $axiom$
\end{definition}

\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})

Feel free to add or delete properties from this list. The list below may contain properties that are not relevant to the class that is being described.

\begin{tabular}{|ll|}\hline
  Classtype                       & second-order \\\hline
  Locally finite                  & \\\hline
  Residual size                   & \\\hline
  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
  Strong amalgamation property    & \\\hline
  Epimorphisms are surjective     & \\\hline
\end{tabular}
\end{properties}
\end{table}

\begin{finite_members} Same as for \href{Distributive_lattices.pdf}{distributive lattices}
\end{finite_members}

\begin{subclasses}\ 

  \href{....pdf}{...} subvariety

  \href{....pdf}{...} expansion

\end{subclasses}

\begin{superclasses}\ 

  \href{....pdf}{...} supervariety

  \href{....pdf}{...} subreduct

\end{superclasses}

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%F. Lastname, \emph{Title}, Journal, \textbf{1}, 23--45 \href{http://www.ams.org/mathscinet-getitem?mr=12a:08034}{MRreview} 

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\end{document}
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