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arXiv · 2010.14770

Strongly NIP almost real closed fields

Lothar Sebastian Krapp·Salma Kuhlmann·Gabriel Lehéricy
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Abstract

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.

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Lothar Sebastian Krapp, Salma Kuhlmann, Gabriel Lehéricy. 2020-10-27. Strongly NIP almost real closed fields. https://doi.org/10.1002/malq.202000060

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