Journal of Symbolic Logic

Existentially Closed Algebras and Boolean Products

Herbert H. J. Riedel

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Abstract

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.

Article information

Source
J. Symbolic Logic, Volume 53, Issue 2 (1988), 571-596.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183742643

Mathematical Reviews number (MathSciNet)
MR947860

Zentralblatt MATH identifier
0677.03023

JSTOR
links.jstor.org

Citation

Riedel, Herbert H. J. Existentially Closed Algebras and Boolean Products. J. Symbolic Logic 53 (1988), no. 2, 571--596. https://projecteuclid.org/euclid.jsl/1183742643


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