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March 2013 Mutually algebraic structures and expansions by predicates
Michael C. Laskowski
J. Symbolic Logic 78(1): 185-194 (March 2013). DOI: 10.2178/jsl.7801120

Abstract

We introduce the notions of a mutually algebraic structures and theories and prove many equivalents. A theory $T$ is mutually algebraic if and only if it is weakly minimal and trivial if and only if no model $M$ of $T$ has an expansion $(M,A)$ by a unary predicate with the finite cover property. We show that every structure has a maximal mutually algebraic reduct, and give a strong structure theorem for the class of elementary extensions of a fixed mutually algebraic structure.

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Michael C. Laskowski. "Mutually algebraic structures and expansions by predicates." J. Symbolic Logic 78 (1) 185 - 194, March 2013. https://doi.org/10.2178/jsl.7801120

Information

Published: March 2013
First available in Project Euclid: 23 January 2013

zbMATH: 1261.03119
MathSciNet: MR3087069
Digital Object Identifier: 10.2178/jsl.7801120

Rights: Copyright © 2013 Association for Symbolic Logic

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Vol.78 • No. 1 • March 2013
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