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

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

2011-06-11

arxiv.org/abs/1106.2203v3

Mathematics

Rings and Algebras

Presented on International conference "Order, Algebra and Logics", Vanderbilt University, 12-16 June, 2007 25 pages, 2 figures

Scientific paper

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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