Lattices of quasi-equational theories as congruence lattices of semilattices with operators, part II
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Date
2012
Authors
Adaricheva, Kira
Nation, J.B.
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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 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). 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 xes both 0 and 1, then there is a quasivariety W such
that the lattice of theories of W is isomorphic to Con(S;+; 0; G).
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Keywords
Research Subject Categories::MATHEMATICS, lattices of quasi-equational theories
Citation
Adaricheva Kira, Nation J. B.; 2012; Lattices of quasi-equational theories as congruence lattices of semilattices with operators, part II; arXiv.org