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Strongly NIP almost real closed fields
Mathematical Logic Quarterly 67 (3):321-328 (2021)
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.Other Versions
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Citations of this work
Definability of Henselian Valuations by Conditions on the Value Group.Lothar Sebastian Krapp, Salma Kuhlmann & Moritz Link - 2023 - Journal of Symbolic Logic 88 (3):1064-1082.
Algebraic and Model Theoretic Properties of O-minimal Exponential Fields.Lothar Sebastian Krapp - 2021 - Bulletin of Symbolic Logic 27 (4):529-530.
References found in this work
Definability and decision problems in arithmetic.Julia Robinson - 1949 - Journal of Symbolic Logic 14 (2):98-114.
Dp-Minimality: Basic Facts and Examples.Alfred Dolich, John Goodrick & David Lippel - 2011 - Notre Dame Journal of Formal Logic 52 (3):267-288.
Dp-minimal valued fields.Franziska Jahnke, Pierre Simon & Erik Walsberg - 2017 - Journal of Symbolic Logic 82 (1):151-165.
The canonical topology on dp-minimal fields.Will Johnson - 2018 - Journal of Mathematical Logic 18 (2):1850007.
On dp-minimality, strong dependence and weight.Alf Onshuus & Alexander Usvyatsov - 2011 - Journal of Symbolic Logic 76 (3):737 - 758.
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