Mutually algebraic structures and expansions by predicates

2012/06/26 by M. Laskowski, Michael C. Laskowski, Laskowski, Michael C.
Computer Science · Mathematics · #03C10 (Primary) 03C45 (Secondary) #Advanced Algebra and Logic #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03C10 #msc:03C45

paper · pdf · doi:10.48550/arxiv.1206.6023

Incorporated comments and suggestions of the anonymous referee. 16 pages

openalex publication_date 2012/06/26 · arxiv created 2012/07/24 · arxiv updated 2012/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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