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arXiv · 1106.2203

Lattices of quasi-equational theories as congruence lattices of semilattices with operators, Part I

Kira Adaricheva·J. B. Nation
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Abstract

We show that for every quasivariety K of structures (where both functions and relations are allowed) there is a semilattice S with operators such that the lattice of quasi-equational theories of K (the dual of the lattice of sub-quasivarieties of K) is isomorphic to Con(S,+,0,F). As a consequence, new restrictions on the natural quasi-interior operator on lattices of quasi-equational theories are found.

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Kira Adaricheva, J. B. Nation. 2012-02-28. Lattices of quasi-equational theories as congruence lattices of semilattices with operators, Part I. https://doi.org/10.1142/s0218196712500658

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