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Preprint Number 1869

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1869. Lothar Sebastian Krapp, Salma Kuhlmann, Gabriel Lehéricy
Strongly NIP almost real closed fields

Submission date: 27 October 2020


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.

Mathematics Subject Classification: 03C45, 03C64, 03C60, 12J10, 12L12

Keywords and phrases:

Full text arXiv 2010.14770: pdf, ps.

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