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kleene_lattices [2010/07/29 18:30]
127.0.0.1 external edit
kleene_lattices [2010/09/04 17:04] (current)
jipsen
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Abbreviation: **KLat** Abbreviation: **KLat**
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====Definition==== ====Definition====
A \emph{Kleene lattice} is a structure $\mathbf{A}=\langle A,\vee A \emph{Kleene lattice} is a structure $\mathbf{A}=\langle A,\vee
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$\langle A,\vee ,\wedge \rangle $ is a lattice $\langle A,\vee ,\wedge \rangle $ is a lattice
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==Morphisms== ==Morphisms==
-Let $\mathbf{A}$ and $\mathbf{B}$ be Kleene lattices. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:Aarrow B$ that is a+Let $\mathbf{A}$ and $\mathbf{B}$ be Kleene lattices.  
 +A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\to B$ that is a
homomorphism: homomorphism:
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\mbox{and}  h(x\cdot y)=h(x)\cdot h(y)$, $h(x^{\ast \mbox{and}  h(x\cdot y)=h(x)\cdot h(y)$, $h(x^{\ast
})=h(x)^{\ast }$, $h(0)=0$, $h(1)=1$ })=h(x)^{\ast }$, $h(0)=0$, $h(1)=1$
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====Examples==== ====Examples====
Example 1: Example 1:
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====Basic results==== ====Basic results====
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====Properties==== ====Properties====
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^[[Strong amalgamation property]]  | | ^[[Strong amalgamation property]]  | |
^[[Epimorphisms are surjective]]  | | ^[[Epimorphisms are surjective]]  | |
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====Finite members==== ====Finite members====
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f(6)= &1488\\ f(6)= &1488\\
\end{array}$ \end{array}$
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====Subclasses==== ====Subclasses====
[[Action lattices]] [[Action lattices]]
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====Superclasses==== ====Superclasses====
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====References==== ====References====
-[(Ln19xx> 
-)]