{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T20:15:10Z","timestamp":1776888910985,"version":"3.51.2"},"reference-count":31,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2009,8]]},"abstract":"<jats:p> A class [Formula: see text] of algebras with a distinguished constant term 0 is called Fregean if congruences of algebras in [Formula: see text] are uniquely determined by their 0\u2013cosets and \u0398<jats:sub>A<\/jats:sub> (0,a) = \u0398<jats:sub>A<\/jats:sub> (0,b) implies a = b for all [Formula: see text]. The structure of Fregean varieties is investigated. In particular it is shown that every congruence permutable Fregean variety consists of algebras that are expansions of equivalential algebras, i.e. algebras that form an algebraization of the purely equivalential fragment of the intuitionistic propositional logic. Moreover the clone of polynomials of any finite algebra A from a congruence permutable Fregean variety is uniquely determined by the congruence lattice of A together with the commutator of congruences. Actually we show that such an algebra A itself can be recovered (up to polynomial equivalence) from its congruence lattice expanded by the commutator, i.e. the structure ( Con (A); \u2227, \u2228, [\u00b7,\u00b7]). This leads to Fregean frames, a notion that generalizes Kripke frames for intuitionistic propositional logic. <\/jats:p>","DOI":"10.1142\/s0218196709005251","type":"journal-article","created":{"date-parts":[[2009,9,3]],"date-time":"2009-09-03T07:03:24Z","timestamp":1251961404000},"page":"595-645","source":"Crossref","is-referenced-by-count":22,"title":["FREGEAN VARIETIES"],"prefix":"10.1142","volume":"19","author":[{"given":"PAWE\u0141","family":"IDZIAK","sequence":"first","affiliation":[{"name":"Theoretical Computer Science Department, Jagiellonian University, Krak\u00f3w, Poland"}]},{"given":"KATARZYNA","family":"S\u0141OMCZY\u0143SKA","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Pedagogical University, Krak\u00f3w, Poland"}]},{"given":"ANDRZEJ","family":"WRO\u0143SKI","sequence":"additional","affiliation":[{"name":"Department of Logic, Jagiellonian University, Krak\u00f3w, Poland"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700002998"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01203370"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BF02483723"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01195727"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01188178"},{"key":"rf6","series-title":"Memoirs of the American Mathematical Society","volume-title":"Algebraizable Logics","volume":"396","author":"Blok W. 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