Journal of Symbolic Logic

Mutually algebraic structures and expansions by predicates

Michael C. Laskowski

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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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J. Symbolic Logic, Volume 78, Issue 1 (2013), 185-194.

First available in Project Euclid: 23 January 2013

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Laskowski, Michael C. Mutually algebraic structures and expansions by predicates. J. Symbolic Logic 78 (2013), no. 1, 185--194. doi:10.2178/jsl.7801120.

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