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Modularity and distributivity of the lattice of Σ -closed subsets of an algebraic structure

Ivan Chajda, Petr Emanovský (1995)

Mathematica Bohemica

Let 𝒜 = ( A , F , R ) be an algebraic structure of type τ and Σ a set of open formulas of the first order language L ( τ ) . The set C Σ ( 𝒜 ) of all subsets of A closed under Σ forms the so called lattice of Σ -closed subsets of 𝒜 . We prove various sufficient conditions under which the lattice C Σ ( 𝒜 ) is modular or distributive.

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