Finite basis problems and results for quasivarieties
 Miklós Maróti,
 Ralph McKenzie
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Let \(\mathcal{K}\) be a finite collection of finite algebras of finite signature such that SP(\(\mathcal{K}\)) has meet semidistributive congruence lattices. We prove that there exists a finite collection \(\mathcal{K}\) _{1} of finite algebras of the same signature, \(\mathcal{K}_1 \supseteq \mathcal{K}\), such that SP(\(\mathcal{K}\) _{1}) is finitely axiomatizable.We show also that if \(HS(\mathcal{K}) \subseteq SP(\mathcal{K})\), then SP(\(\mathcal{K}\) _{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.
 Title
 Finite basis problems and results for quasivarieties
 Journal

Studia Logica
Volume 78, Issue 12 , pp 293320
 Cover Date
 200411
 DOI
 10.1007/s1122500533205
 Print ISSN
 00393215
 Online ISSN
 15728730
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 quasivarieties
 finite axiomatizability
 pseudocomplemented congruence lattices
 Willard terms
 Authors

 Miklós Maróti ^{(1)}
 Ralph McKenzie ^{(1)}
 Author Affiliations

 1. Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, 37240, Nashville, Tennessee, USA