DEFINABLE HENSELIAN VALUATIONS

DOI10.1017/jsl.2014.64zbMath1372.03078arXiv1210.7615OpenAlexW1993703767MaRDI QIDQ5251359

Jochen Koenigsmann, Franziska Jahnke

Publication date: 20 May 2015

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.7615

zbMATH Keywords

valuationsabsolute Galois groupsHenselian valued fieldsdefinable valuations

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Interpolation, preservation, definability (03C40) Model theory of fields (12L12) Valued fields (12J10)

Related Items (13)

Ordered fields dense in their real closure and definable convex valuations ⋮ Distality in valued fields and related structures ⋮ On the quantifier complexity of definable canonical Henselian valuations ⋮ A definable Henselian valuation with high quantifier complexity ⋮ DEFINABILITY OF HENSELIAN VALUATIONS BY CONDITIONS ON THE VALUE GROUP ⋮ Definable V-topologies, Henselianity and NIP ⋮ Definable Valuations Induced by Definable Subgroups ⋮ Recent progress on definability of Henselian valuations ⋮ Definable valuations induced by multiplicative subgroups and NIP fields ⋮ Onn-dependent groups and fields ⋮ A CONJECTURAL CLASSIFICATION OF STRONGLY DEPENDENT FIELDS ⋮ Strongly dependent ordered abelian groups and Henselian fields ⋮ Uniform definability of henselian valuation rings in the Macintyre language:

Cites Work

• Uniformly defining valuation rings in Henselian valued fields with finite or pseudo-finite residue fields
• On finitely generated profinite groups. I: Strong completeness and uniform bounds. II: Products in quasisimple groups.
• Characterization of fans and hereditarily pythagorean fields
• Artin-Schreier extensions in NIP and simple fields
• \(p\)-Henselian fields
• Definable non-divisible Henselian valuations
• Unnamed Item

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