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.
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 Title
 Finite basis problems and results for quasivarieties
 Journal

Studia Logica
Volume 78, Issue 12 , pp 293320
 Cover Date
 20041101
 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