Strongly NIP almost real closed fields
arXiv:2010.14770 · doi:10.1002/malq.202000060
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.
To appear in MLQ Math. Log. Q. A previous version of this preprint was part of arXiv:1810.10377. arXiv admin note: text overlap with arXiv:2010.11832