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A monotonicity theorem for dp-minimal densely ordered groups

Published online by Cambridge University Press:  12 March 2014

John Goodrick
John Goodrick*
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA, E-mail: [email protected]
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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).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 1 , March 2010 , pp. 221 - 238
Copyright
Copyright © Association for Symbolic Logic 2010

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