Adaricheva, KiraNation, J. B.2016-02-092016-02-092012Adaricheva Kira, Nation J.B.; 2012; Lattices of quasi-equational theories as congruence lattices of semilattices with operators, part I; arXiv.orghttp://nur.nu.edu.kz/handle/123456789/1206We 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.enAttribution-NonCommercial-ShareAlike 3.0 United StatesResearch Subject Categories::MATHEMATICSlattices of quasi-equational theoriesArticle