Journal of Symbolic Logic

Existentially Closed Algebras and Boolean Products

Herbert H. J. Riedel

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A Boolean product construction is used to give examples of existentially closed algebras in the universal Horn class ISP$(K)$ generated by a universal class $K$ of finitely subdirectly irreducible algebras such that $\Gamma^a(K)$ has the Fraser-Horn property. If $\lbrack a \neq b\rbrack \cap \lbrack c \neq d\rbrack = \varnothing$ is definable in $K$ and $K$ has a model companion of $K$-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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J. Symbolic Logic, Volume 53, Issue 2 (1988), 571-596.

First available in Project Euclid: 6 July 2007

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Riedel, Herbert H. J. Existentially Closed Algebras and Boolean Products. J. Symbolic Logic 53 (1988), no. 2, 571--596.

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