## Journal of Symbolic Logic

### Existentially Closed Algebras and Boolean Products

Herbert H. J. Riedel

#### 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