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arXiv · 1810.10377

On Strongly NIP Ordered Fields and Definable Convex Valuations

Lothar Sebastian Krapp·Salma Kuhlmann·Gabriel Lehéricy
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Abstract

We investigate what henselian valuations on ordered fields are definable in the language of ordered rings. This leads towards a systematic study of the class of ordered fields which are dense in their real closure. Some results have connections to recent conjectures on definability of henselian valuations in strongly NIP fields. Moreover, we obtain a complete characterisation of strongly NIP almost real closed fields.

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Lothar Sebastian Krapp, Salma Kuhlmann, Gabriel Lehéricy. 2018-10-24. On Strongly NIP Ordered Fields and Definable Convex Valuations. https://arxiv.org/abs/1810.10377

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