Abstract

AbstractA Boolean product construction is used to give examples of existentially closed algebras in the universal Horn class ISP(K) generated by a universal classKof finitely subdirectly irreducible algebras such that Γa(K) has the Fraser-Horn property. If ⟦a≠b⟧ ∩ ⟦c≠d⟧ = ∅ is definable inKandKhas a model companion ofK-simple algebras, then it is shown that ISP(K) has a model companion. Conversely, a sufficient condition is given for ISP(K) to have no model companion.

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