Studia Logica

, Volume 78, Issue 1, pp 293–320

Finite basis problems and results for quasivarieties

  • Miklós Maróti
  • Ralph McKenzie
Article

DOI: 10.1007/s11225-005-3320-5

Cite this article as:
Maróti, M. & McKenzie, R. Stud Logica (2004) 78: 293. doi:10.1007/s11225-005-3320-5

Abstract

Let \(\mathcal{K}\) be a finite collection of finite algebras of finite signature such that SP(\(\mathcal{K}\)) has meet semi-distributive 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.

Keywords

quasivarietiesfinite axiomatizabilitypseudo-complemented congruence latticesWillard terms

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Miklós Maróti
    • 1
  • Ralph McKenzie
    • 1
  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA