Abstract
In [21], D. Pigozzi has proved in a non-constructive way that every relatively congruence distributive quasivariety of finite type generated by a finite set of finite algebras is finitely axiomatizable. In this paper we show that the non-constructive parts of Pigozzi's argument can be replaced by constructive ones. As a result we obtain a method of constructing a finite set of quasi-equational axioms for each relatively congruence distributive quasivariety generated by a given finite set of finite algebras of finite type. The method can also be applied to finitely generated congruence distributive varieties.
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Dziobiak, W. Finite bases for finitely generated, relatively congruence distributive quasivarieties. Algebra Universalis 28, 303–323 (1991). https://doi.org/10.1007/BF01191083
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DOI: https://doi.org/10.1007/BF01191083