Strongly dependent ordered abelian groups and Henselian fields

DOI10.1007/s11856-019-1885-3zbMath1454.03043arXiv1706.03376OpenAlexW2963491230MaRDI QIDQ2317695

Assaf Hasson, Yatir Halevi

Publication date: 12 August 2019

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.03376

zbMATH Keywords

Henselian fieldsordered abelian groups

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Classification theory, stability, and related concepts in model theory (03C45) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20) Model theory of fields (12L12) Valued fields (12J10)

Related Items (14)

Ordered fields dense in their real closure and definable convex valuations ⋮ Distality in valued fields and related structures ⋮ Dp-finite fields. I(B): Positive characteristic ⋮ Interpretable fields in various valued fields ⋮ Strongly NIP almost real closed fields ⋮ Mini-workshop: Topological and differential expansions of o-minimal structures. Abstracts from the mini-workshop held November 27 -- December 3, 2022 ⋮ DEFINABILITY OF HENSELIAN VALUATIONS BY CONDITIONS ON THE VALUE GROUP ⋮ ELIMINATION OF IMAGINARIES IN ORDERED ABELIAN GROUPS WITH BOUNDED REGULAR RANK ⋮ The classification of dp-minimal and dp-small fields ⋮ Eliminating field quantifiers in strongly dependent henselian fields ⋮ Some remarks on inp-minimal and finite burden groups ⋮ Definable valuations induced by multiplicative subgroups and NIP fields ⋮ THE DP-RANK OF ABELIAN GROUPS ⋮ Fields with a dense-codense linearly independent multiplicative subgroup

Cites Work

• Strongly dependent theories
• Chain conditions in dependent groups
• Quantifier elimination in ordered abelian groups
• Types in valued fields with coefficient maps
• Quantifier elimination for Henselian fields relative to additive and multiplicative congruences
• Artin-Schreier extensions in NIP and simple fields
• NIP Henselian valued fields
• Dependent first order theories, continued
• Some model theory for almost real closed fields
• A Characterization of Strongly Dependent Ordered Abelian Groups
• Eliminating field quantifiers in strongly dependent henselian fields
• The Theory of Ordered Abelian Groups does not have the Independence Property
• THE DP-RANK OF ABELIAN GROUPS
• DEFINABLE HENSELIAN VALUATIONS
• Lectures on the Model Theory of Valued Fields
• Defining Coarsenings of Valuations
• Definable non-divisible Henselian valuations
• Valued Fields
• DP-MINIMAL VALUED FIELDS
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