Submission date: 7 March 2019

Abstract:

In this paper, we undertake a systematic model and valuation theoretic study of the class of ordered fields which are dense in their real closure. We apply this study to determine definable henselian valuations on ordered fields, in the language of ordered rings. In light of our results, we re-examine recent conjectures in the context of strongly NIP ordered fields.

Mathematics Subject Classification: Primary 12J15, 03C64; Secondary 06F20, 12J10.

Keywords and phrases: regular densely ordered abelian groups, convex subgroups, henselian valuations, almost real closed fields, Hahn groups and fields, normal integer parts, strongly NIP ordered fields

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