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A monotonicity theorem for dp-minimal densely ordered groups. (English) Zbl 1184.03035

Summary: 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, 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.

MSC:

03C64 Model theory of ordered structures; o-minimality
06F15 Ordered groups
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References:

[1] Scientiae Mathematicae Japonicae 59 pp 265– (2004)
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