Article
MSC:
03C05,
04A05,
06A23,
06B10,
06C05,
06D05,
08A05 | MR 1357603 | Zbl 0833.08002 | DOI: 10.21136/MB.1995.126220
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Keywords:
closure system; distributive lattice; lattices of $\Sigma-closed subsets; modular lattice; algebraic structures; $\Sigma$-closed subset; convex subset
closure system; distributive lattice; lattices of $\Sigma-closed subsets; modular lattice; algebraic structures; $\Sigma$-closed subset; convex subset
Summary:
Let $\Cal A =(A,F,R)$ be an algebraic structure of type $\tau$ and $\Sigma$ a set of open formulas of the first order language $L(\tau)$. The set $C_\Sigma(\Cal A)$ of all subsets of $A$ closed under $\Sigma$ forms the so called lattice of $\Sigma$-closed subsets of $\Cal A$. We prove various sufficient conditions under which the lattice $C_\Sigma(\Cal A)$ is modular or distributive.
References:
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