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Preprint Number 1505

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1505. Lothar Sebastian Krapp and Salma Kuhlmann
On Strongly NIP Ordered Fields
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Submission date: 24 October 2018

Abstract:

The following conjecture is due to Shelah-Hasson: Any infinite strongly NIP field is either real closed, algebraically closed, or it admits a non-trivial definable henselian valuation, in the language L_r = { + , - , ⋅ , 0 , 1 }. Inspired by this, we formulate an analogous conjecture for ordered fields in the language L_{or} = L_r ∪ { < }. Moreover, we examine strongly NIP almost real closed fields as well as ordered Hahn fields and exhibit connections to ordered fields which are not dense in their real closure and dp-minimal ordered fields.

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Full text arXiv 1810.10377: pdf, ps.


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