Journal of Symbolic Logic

Complete Theories with Only Universal and Existential Axioms

A. H. Lachlan

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Abstract

Let $T$ be a complete first-order theory over a finite relational language which is axiomatized by universal and existential sentences. It is shown that $T$ is almost trivial in the sense that the universe of any model of $T$ can be written $F \overset{\cdot}{\cup} I_1 \overset{\cdot}{\cup} I_2 \overset{\cdot}{\cup} \cdots \overset{\cdot}{\cup} I_n$, where $F$ is finite and $I_1, I_2,\ldots,I_n$ are mutually indiscernible over $F$. Some results about complete theories with $\exists\forall$-axioms over a finite relational language are also mentioned.

Article information

Source
J. Symbolic Logic, Volume 52, Issue 3 (1987), 698-711.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183742437

Mathematical Reviews number (MathSciNet)
MR902985

Zentralblatt MATH identifier
0637.03024

JSTOR
links.jstor.org

Citation

Lachlan, A. H. Complete Theories with Only Universal and Existential Axioms. J. Symbolic Logic 52 (1987), no. 3, 698--711. https://projecteuclid.org/euclid.jsl/1183742437


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