Abstract
We consider varieties with the property that the intersection of any pair of principal congruences is finitely generated, and, in fact, generated by pairs of terms constructed from the generators of the principal components in a uniform way. We say that varieties with this property haveequationally definable principal meets (EDPM). There are many examples of these varieties occurring in the literature, especially in connection with metalogical investigations. The main result of this paper is that every finite, subdirectly irreducible member of a variety with EDPM generates a finitely based quasivariety. This is proved in Section 2. In the first section we prove that every variety with EDPM is congruence-distributive.
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Blok, W.J., Pigozzi, D. A finite basis theorem for quasivarieties. Algebra Universalis 22, 1–13 (1986). https://doi.org/10.1007/BF01190734
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DOI: https://doi.org/10.1007/BF01190734