Finite basis problems and results for quasivarieties

Maróti, Miklós and McKenzie, Ralph (2004) Finite basis problems and results for quasivarieties. Studia Logica, 78 (1-2). pp. 293-320. ISSN 0039-3215

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Abstract

Let K be a finite collection of finite algebras of finite signature such that SP( K ) has meet semi-distributive congruence lattices. We prove that there exists a finite collection K 1 of finite algebras of the same signature, K1⊇K , such that SP( K 1) is finitely axiomatizable.We show also that if HS(K)⊆SP(K) , then SP( K 1) is finitely axiomatizable. We offer new proofs of two important finite basis theorems of D. Pigozzi and R. Willard. Our actual results are somewhat more general than this abstract indicates.

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