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Definable valuations induced by multiplicative subgroups and NIP fields
Archive for Mathematical Logic 58 (7-8):819-839 (2019)
Abstract
We study the algebraic implications of the non-independence property and variants thereof on infinite fields, motivated by the conjecture that all such fields which are neither real closed nor separably closed admit a henselian valuation. Our results mainly focus on Hahn fields and build up on Will Johnson’s “The canonical topology on dp-minimal fields” :1850007, 2018).Other Versions
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Citations of this work
Strongly NIP almost real closed fields.Lothar Sebastian Krapp, Salma Kuhlmann & Gabriel Lehéricy - 2021 - Mathematical Logic Quarterly 67 (3):321-328.
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.
References found in this work
Theories without the tree property of the second kind.Artem Chernikov - 2014 - Annals of Pure and Applied Logic 165 (2):695-723.
The canonical topology on dp-minimal fields.Will Johnson - 2018 - Journal of Mathematical Logic 18 (2):1850007.
Definable Henselian valuations.Franziska Jahnke & Jochen Koenigsmann - 2015 - Journal of Symbolic Logic 80 (1):85-99.
Uniformly defining p-henselian valuations.Franziska Jahnke & Jochen Koenigsmann - 2015 - Annals of Pure and Applied Logic 166 (7-8):741-754.
Superrosy dependent groups having finitely satisfiable generics.Clifton Ealy, Krzysztof Krupiński & Anand Pillay - 2008 - Annals of Pure and Applied Logic 151 (1):1-21.
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