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Congruence distributive quasivarieties whose finitely subdirectly irreducible members form a universal class

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Abstract

By a congruence distributive quasivariety we mean any quasivarietyK of algebras having the property that the lattices of those congruences of members ofK which determine quotient algebras belonging toK are distributive. This paper is an attempt to study congruence distributive quasivarieties with the additional property that their classes of relatively finitely subdirectly irreducible members are axiomatized by sets of universal sentences. We deal with the problem of characterizing such quasivarieties and the problem of their finite axiomatizability.

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Authors and Affiliations

  1. Section of Logic, Polish Academy of Sciences, Lódź, Poland

    Janusz Czelakowski & Wiesław Dziobiak

  2. Institute of Mathematics, N. Copernicus University, Toruń, Poland

    Janusz Czelakowski & Wiesław Dziobiak

Authors
  1. Janusz Czelakowski
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  2. Wiesław Dziobiak
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To the memory of Basia Czelakowska.

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Czelakowski, J., Dziobiak, W. Congruence distributive quasivarieties whose finitely subdirectly irreducible members form a universal class. Algebra Universalis 27, 128–149 (1990). https://doi.org/10.1007/BF01190258

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  • DOI: https://doi.org/10.1007/BF01190258

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