Journal of Symbolic Logic

A monotonicity theorem for dp-minimal densely ordered groups

John Goodrick

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Abstract

Dp-minimality is a common generalization of weak minimality and weak o-minimality. If T is a weakly o-minimal theory then it is dp-minimal (Fact 2.2), but there are dp-minimal densely ordered groups that are not weakly o-minimal. We introduce the even more general notion of inp-minimality and prove that in an inp-minimal densely ordered group, every definable unary function is a union of finitely many continuous locally monotonic functions (Theorem 3.2).

Article information

Source
J. Symbolic Logic, Volume 75, Issue 1 (2010), 221-238.

Dates
First available in Project Euclid: 25 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1264433917

Digital Object Identifier
doi:10.2178/jsl/1264433917

Mathematical Reviews number (MathSciNet)
MR2605890

Zentralblatt MATH identifier
1184.03035

Citation

Goodrick, John. A monotonicity theorem for dp-minimal densely ordered groups. J. Symbolic Logic 75 (2010), no. 1, 221--238. doi:10.2178/jsl/1264433917. https://projecteuclid.org/euclid.jsl/1264433917


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