## Journal of Symbolic Logic

### Mutually algebraic structures and expansions by predicates

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 23 January 2013

https://projecteuclid.org/euclid.jsl/1358951107

Digital Object Identifier
doi:10.2178/jsl.7801120

Mathematical Reviews number (MathSciNet)
MR3087069

Zentralblatt MATH identifier
1261.03119

#### Citation

Laskowski, Michael C. Mutually algebraic structures and expansions by predicates. J. Symbolic Logic 78 (2013), no. 1, 185--194. doi:10.2178/jsl.7801120. https://projecteuclid.org/euclid.jsl/1358951107