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Expansion of a model of a weakly o-minimal theory by a family of unary predicates

Published online by Cambridge University Press:  12 March 2014

Bektur Sembiuly Baizhanov
Bektur Sembiuly Baizhanov*
Affiliation:
Institute of Informatics, and Control Problems, Ul.Poushkina, 125, 480100 Almaty, Kazakhstan, E-mail: baizhanov@hotmail.com, E-mail: baijan@ipic.academ.alma-ata.su
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Abstract

A subset A ⊆ M of a totally ordered structure M is said to be convex, if for any a, b ∈ A: [a < b → ∀t (a < tb → t ∈ A)]. A complete theory of first order is weakly o-minimal (M. Dickmann [D]) if any model M is totally ordered by some ∅-definable formula and any subset of M which is definable with parameters from M is a finite union of convex sets. We prove here that for any model M of a weakly o-minimal theory T. any expansion M+ of M by a family of unary predicates has a weakly o-minimal theory iff the set of all realizations of each predicate is a union of a finite number of convex sets (Theorem 63). that solves the Problem of Cherlin-Macpherson-Marker-Steinhorn [MMS] for the class of weakly o-minimal theories.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 3 , September 2001 , pp. 1382 - 1414
Copyright
Copyright © Association for Symbolic Logic 2001

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