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ARTIN–SCHREIER EXTENSIONS AND COMBINATORIAL COMPLEXITY IN HENSELIAN VALUED FIELDS

Part of: Model theory Connections with logic

Published online by Cambridge University Press:  03 September 2024

BLAISE BOISSONNEAU Open the ORCID record for BLAISE BOISSONNEAU [Opens in a new window]
BLAISE BOISSONNEAU*
Affiliation:
DÉPARTEMENT DE MATHÉMATIQUES ACADÉMIE DE PARIS 12, BOULEVARD D’INDOCHINE 75019 PARIS, FRANCE
*
E-mail: [email protected]
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Abstract

We give explicit formulas witnessing IP, IP$_{\!n}$, or TP2 in fields with Artin–Schreier extensions. We use them to control p-extensions of mixed characteristic henselian valued fields, allowing us most notably to generalize to the NIP$_{\!n}$ context one way of Anscombe–Jahnke’s classification of NIP henselian valued fields. As a corollary, we obtain that NIP$_{\!n}$ henselian valued fields with NIP residue field are NIP. We also discuss tameness results for NTP2 henselian valued fields.

Keywords

logicmodel theoryvalued fieldshenselianityArtin–Schreier extensionNIPNIPnNTP2

MSC classification

Primary: 03C45: Classification theory, stability and related concepts 03C60: Model-theoretic algebra 12L12: Model theory
Type
Article
Information
The Journal of Symbolic Logic , Volume 89 , Issue 4 , December 2024 , pp. 1747 - 1767
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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