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March 2010 A monotonicity theorem for dp-minimal densely ordered groups
John Goodrick
J. Symbolic Logic 75(1): 221-238 (March 2010). DOI: 10.2178/jsl/1264433917

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).

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John Goodrick. "A monotonicity theorem for dp-minimal densely ordered groups." J. Symbolic Logic 75 (1) 221 - 238, March 2010. https://doi.org/10.2178/jsl/1264433917

Information

Published: March 2010
First available in Project Euclid: 25 January 2010

zbMATH: 1184.03035
MathSciNet: MR2605890
Digital Object Identifier: 10.2178/jsl/1264433917

Rights: Copyright © 2010 Association for Symbolic Logic

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Vol.75 • No. 1 • March 2010
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