Lothar Sebastian Krapp, Salma Kuhlmann, Gabriel Lehéricy
Published 2020-10-27Version 1
The following conjecture is due to Shelah-Hasson: Any infinite strongly NIP field is either real closed, algebraically closed, or admits a non-trivial definable henselian valuation, in the language of rings. We specialise this conjecture to ordered fields in the language of ordered rings, which leads towards a systematic study of the class of strongly NIP almost real closed fields. As a result, we obtain a complete characterisation of this class.
Comments: A previous version of this preprint was part of arXiv:1810.10377. arXiv admin note: text overlap with arXiv:2010.11832
On definable groups in real closed fields with a generic derivation, and related structures: I
The domination monoid in o-minimal theories
Definable henselian valuations in positive residue characteristic
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