=====Ockham algebras=====

Abbreviation: **OckA**
====Definition====
An \emph{Ockham algebra} is a structure $\mathbf{A}=\langle A,\vee
,0,\wedge ,1,'\rangle $ such that


$\langle A,\vee ,0,\wedge ,1\rangle $ is a bounded distributive
lattice


$'$ is a dual endomorphism:  
$(x\wedge y)' =x'\vee y'$, $
(x\vee y)' =x'\wedge y'$, $
0'=1$, $1'=0$
==Morphisms==
Let $\mathbf{A}$ and $\mathbf{B}$ be Ockham algebras. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a
homomorphism: 

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

====Examples====
Example 1: 

====Basic results====

====Properties====
^[[Classtype]]  |Variety |
^[[Equational theory]]  | |
^[[Quasiequational theory]]  | |
^[[First-order theory]]  | |
^[[Congruence distributive]]  |Yes |
^[[Congruence modular]]  |Yes |
^[[Congruence n-permutable]]  | |
^[[Congruence regular]]  | |
^[[Congruence uniform]]  | |
^[[Congruence extension property]]  | |
^[[Definable principal congruences]]  | |
^[[Equationally def. pr. cong.]]  | |
^[[Amalgamation property]]  | |
^[[Strong amalgamation property]]  | |
^[[Epimorphisms are surjective]]  | |
^[[Locally finite]]  | |
^[[Residual size]]  | |
====Finite members====

$\begin{array}{lr}
f(1)= &1\\
f(2)= &1\\
f(3)= &2\\
f(4)= &\\
f(5)= &\\
f(6)= &\\
f(7)= &\\
f(8)= &\\
f(9)= &\\
f(10)= &\\
\end{array}$

====Subclasses====
[[De Morgan algebras]] 

====Superclasses====
[[Bounded distributive lattices]] 


====References====

[(Ln19xx>
)]\end{document}
%</pre>