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arXiv · 1106.2204

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

Kira Adaricheva·J. B. Nation
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Abstract

Part I proved that for every quasivariety K of structures (which may have both operations and relations) there is a semilattice S with operators such that he lattice of quasi-equational theories of K (the dual of the lattice of sub-quasivarieties of K) is isomorphic to Con(S,+,0,F). It is known that if S is a join semilattice with 0 (and no operators), then there is a quasivariety Q such that the lattice of theories of Q is isomorphic to Con(S,+,0). We prove that if S is a semilattice having both 0 and 1 with a group G of operators acting on S, and each operator in G fixes both 0 and 1, then there is a quasivariety W such that the lattice of quasi-equational theories of W is isomorphic to Con(S,+,0,G).

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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 II. https://doi.org/10.1142/s021819671250066x

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