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Preprint Number 471

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471. Michael C. Laskowski
Mutually algebraic structures and expansions by predicates
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Submission date: 26 June 2012.

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.

Mathematics Subject Classification: 03C10 (Primary) 03C45 (Secondary)

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Full text arXiv 1206.6023: pdf, ps.


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