On some extensions of the class of MV-algebras

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Abstract

In the present paper we will ask for the lattice L(MV Ex ) of subvarieties of the variety defined by the set Ex(MV) of all externally compatible identities valid in the variety MV of all MV-algebras. In particular, we will find all subdirectly irreducible algebras from the classes in the lattice L(MV Ex ) and give syntactical and semantical characterization of the class of algebras defined by P-compatible identities of MV-algebras.

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MV-algebra, variety, identity, P-compatible identity, equational base, subdirectly irreducible algebras

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Logic and Logical Philosophy, No. 1, Vol. 25, pp. 35-49

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