A monotonicity theorem for dp-minimal densely ordered groups
John Goodrick
Source: J. Symbolic Logic Volume 75, Issue 1
(2010), 221-238.
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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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1264433917
Digital Object Identifier: doi:10.2178/jsl/1264433917
Zentralblatt MATH identifier: 05681300
Mathematical Reviews number (MathSciNet): MR2605890
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