A monotonicity theorem for dp-minimal densely ordered groups

Journal of Symbolic Logic 75 (1):221-238 (2010)
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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)

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Citations of this work

Theories without the tree property of the second kind.Artem Chernikov - 2014 - Annals of Pure and Applied Logic 165 (2):695-723.
Dp-Minimality: Basic Facts and Examples.Alfred Dolich, John Goodrick & David Lippel - 2011 - Notre Dame Journal of Formal Logic 52 (3):267-288.
The canonical topology on dp-minimal fields.Will Johnson - 2018 - Journal of Mathematical Logic 18 (2):1850007.
Tame Topology over dp-Minimal Structures.Pierre Simon & Erik Walsberg - 2019 - Notre Dame Journal of Formal Logic 60 (1):61-76.
On VC-minimal fields and dp-smallness.Vincent Guingona - 2014 - Archive for Mathematical Logic 53 (5-6):503-517.

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References found in this work

Generic structures and simple theories.Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):71-92.

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