Journal of Symbolic Logic

Model Companions for Finitely Generated Universal Horn Classes

Stanley Burris

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In an earlier paper we proved that a universal Horn class generated by finitely many finite structures has a model companion. If the language has only finitely many fundamental operations then the theory of the model companion admits a primitive recursive elimination of quantifiers and is primitive recursive. The theory of the model companion is $\aleph_0$-categorical iff it is complete iff the universal Horn class has the joint embedding property iff the universal Horn class is generated by a single finite structure. In the last section we look at structure theorems for the model companions of universal Horn classes generated by functionally complete algebras, in particular for the cases of rings and groups.

Article information

J. Symbolic Logic, Volume 49, Issue 1 (1984), 68-74.

First available in Project Euclid: 6 July 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 03C10: Quantifier elimination, model completeness and related topics
Secondary: 03C35: Categoricity and completeness of theories 03C60: Model-theoretic algebra [See also 08C10, 12Lxx, 13L05] 08C10: Axiomatic model classes [See also 03Cxx, in particular 03C60]


Burris, Stanley. Model Companions for Finitely Generated Universal Horn Classes. J. Symbolic Logic 49 (1984), no. 1, 68--74.

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