Studia Logica

, Volume 92, Issue 1, pp 109–120 | Cite as

Quasivarieties with Definable Relative Principal Subcongruences

Article

Abstract

For quasivarieties of algebras, we consider the property of having definable relative principal subcongruences, a generalization of the concepts of definable relative principal congruences and definable principal subcongruences. We prove that a quasivariety of algebras with definable relative principal subcongruences has a finite quasiequational basis if and only if the class of its relative (finitely) subdirectly irreducible algebras is strictly elementary. Since a finitely generated relatively congruence-distributive quasivariety has definable relative principal subcongruences, we get a new proof of the result due to D. Pigozzi: a finitely generated relatively congruence-distributive quasivariety has a finite quasi-equational basis.

Keywords

Quasivariety relatively congruence-distributive quasivariety definable relative principal subcongruences finite quasi-equational basis 

2000 Mathematics Subject Classification

08C15 08A30 08B10 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Institute of MathematicsNational Academy of ScienceBishkekKyrghyz Republic
  2. 2.Faculty of Mathematics and Information SciencesWarsaw University of TechnologyWarsawPoland
  3. 3.Eduard Čech CenterCharles UniversityPragueCzech Republic

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