# Differences

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double_stone_algebras [2010/07/29 15:46] (current)
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+=====Double Stone algebras=====
+Abbreviation: **DblStAlg**
+====Definition====
+A \emph{double Stone algebra} is a structure $\mathbf{L}=\langle L,\vee ,0,\wedge ,1,^*\rangle$ such that
+
+
+$\langle L,\vee,0,\wedge,1,^*\rangle$ is a [[Stone algebras]]
+
+
+$\langle L,\wedge,1,\vee,0,^*\rangle$ is a [[Stone algebras]]
+
+==Morphisms==
+Let $\mathbf{L}$ and $\mathbf{M}$ be double Stone algebras. A morphism from $\mathbf{L}$ to $\mathbf{M}$ is a function $h:L\rightarrow M$ that is a
+homomorphism:
+
+$h(x\vee y)=h(x)\vee h(y)$, $h(x\wedge y)=h(x)\wedge h(y)$, $h(0)=0$, $h(1)=1$, $h(x^*)=h(x)^*$
+
+====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]]  |yes |
+^[[Definable principal congruences]]  | |
+^[[Equationally def. pr. cong.]]  | |
+^[[Amalgamation property]]  | |
+^[[Strong amalgamation property]]  | |
+^[[Epimorphisms are surjective]]  | |
+^[[Locally finite]]  | |
+^[[Residual size]]  | |
+====Finite members====
+
+$\begin{array}{lr} +f(1)= &1\\ +f(2)= &1\\ +f(3)= &1\\ +f(4)= &\\ +f(5)= &\\ +f(6)= &\\ +f(7)= &\\ +\end{array}$
+
+====Subclasses====
+[[Boolean algebras]]
+
+====Superclasses====
+[[Stone algebras]]
+
+
+====References====
+
+[(Ln19xx>
+)]

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