Existentially closed algebras and boolean products

Journal of Symbolic Logic 53 (2):571-596 (1988)
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Abstract

A Boolean product construction is used to give examples of existentially closed algebras in the universal Horn class ISP generated by a universal classKof finitely subdirectly irreducible algebras such that Γa 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 has a model companion. Conversely, a sufficient condition is given for ISP to have no model companion.

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10.1017/s0022481200028474

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Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
On Model-Completeness.Per Lindström - 1964 - Theoria 30 (3):183-196.
Model-completions and modules.P. Eklof - 1971 - Annals of Mathematical Logic 2 (3):251.
Complete Theories.Robert L. Vaught - 1960 - Journal of Symbolic Logic 25 (2):172-174.

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