Strongly NIP almost real closed fields
Lothar Sebastian Krapp, Salma Kuhlmann, Gabriel Leh\'ericy
TL;DR
This paper investigates the structure of strongly NIP ordered fields, providing a complete classification of almost real closed fields within this logical framework, advancing understanding of their algebraic and model-theoretic properties.
Contribution
It offers a complete characterization of strongly NIP almost real closed fields, extending Shelah-Hasson's conjecture to ordered fields and clarifying their structure.
Findings
Characterization of strongly NIP almost real closed fields
Extension of Shelah-Hasson conjecture to ordered fields
Systematic study of strongly NIP ordered fields
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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