Submission date: 10 February 2019.

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.

Mathematics Subject Classification: Primary 03C45, 03C64; Secondary 03C60, 12J10, 12L12.

Keywords and phrases: strongly dependent theories, NIP, almost real closed fields

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