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

Adaricheva K. V.

Gorbunov V.

Hofmann R.

J. B. NATION

KIRA ADARICHEVA

Schmidt E. T.

English

arXiv

 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, 𝒡). 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 theories of 𝒲 is isomorphic to Con(S, +, 0, 𝒢). </jats:p

Crossref

International Journal of Algebra and Computation

LATTICES OF QUASI-EQUATIONAL THEORIES AS CONGRUENCE LATTICES OF SEMILATTICES WITH OPERATORS: PART II

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

Adaricheva, Kira

Nation, J. B.

Nazarbayev University Repository

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

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 ofK (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

Kira Adaricheva

J. B. Nation

CiteSeerX

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

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, 𝒡. As a consequence, new restrictions on the natural quasi-interior operator on lattices of quasi-equational theories are found.</jats:p

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

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

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Nazarbayev University Repository

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