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Mutually algebraic structures and expansions by predicates

Published online by Cambridge University Press:  12 March 2014

Michael C. Laskowski
Michael C. Laskowski*
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742-4015, USA, E-mail: mcl@math.umd.edu
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 1 , March 2013 , pp. 185 - 194
Copyright
Copyright © Association for Symbolic Logic 2013

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References

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