Goodrick, John A monotonicity theorem for dp-minimal densely ordered groups. (English) Zbl 1184.03035 J. Symb. Log. 75, No. 1, 221-238 (2010). 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. Cited in 1 ReviewCited in 11 Documents MSC: 03C64 Model theory of ordered structures; o-minimality 06F15 Ordered groups Keywords:dp-minimality; weak o-minimality; dp-minimal densely ordered groups; inp-minimality PDF BibTeX XML Cite \textit{J. Goodrick}, J. Symb. Log. 75, No. 1, 221--238 (2010; Zbl 1184.03035) Full Text: DOI OpenURL References: [1] Scientiae Mathematicae Japonicae 59 pp 265– (2004) [2] Fundamenta Mathematicae 162 pp 193– (1999) · Zbl 0933.00004 [3] DOI: 10.1016/S0168-0072(98)00021-9 · Zbl 0929.03043 [4] Proceedings of the third Easter conference on model theory pp 64– (1985) [5] DOI: 10.1090/S0002-9947-00-02633-7 · Zbl 0982.03021 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.