Artin-Schreier extensions in NIP and simple fields

DOI10.1007/S11856-011-0104-7zbMath1261.03120arXiv1009.5421OpenAlexW1988226351MaRDI QIDQ1758927

Frank O. Wagner, Itay Kaplan, Thomas J. Scanlon

Publication date: 19 November 2012

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

Full work available at URL: https://arxiv.org/abs/1009.5421

zbMATH Keywords

NIPvalued fieldsArtin-Schreier extensionssimple theories

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Classification theory, stability, and related concepts in model theory (03C45) Non-Archimedean valued fields (12J25) Model theory of fields (12L12) Field extensions (12Fxx)

Related Items (29)

Dp-minimal integral domains ⋮ Distality in valued fields and related structures ⋮ Dp-finite fields. I(A): The infinitesimals ⋮ Interpretable fields in various valued fields ⋮ Type-definable NIP fields are Artin–Schreier closed ⋮ Incidence bounds in positive characteristic via valuations and distality ⋮ Model theory: combinatorics, groups, valued fields and neostability. Abstracts from the workshop held January 8--14, 2023 ⋮ Burden in Henselian valued fields ⋮ Division rings with ranks ⋮ Characterizing NIP henselian fields ⋮ Henselianity in NIP \(\mathbb{F}_p\)-algebras ⋮ The classification of dp-minimal and dp-small fields ⋮ Pseudo-linear algebra over a division ring ⋮ On properties of (weakly) small groups ⋮ Eliminating field quantifiers in strongly dependent henselian fields ⋮ Superrosy fields and valuations ⋮ Fields with few types ⋮ DP-MINIMAL VALUED FIELDS ⋮ GROUPES FINS ⋮ Definable valuations induced by multiplicative subgroups and NIP fields ⋮ NIP Henselian valued fields ⋮ Immediately algebraically closed fields ⋮ VARIATIONS SUR UN THÈME DE ALDAMA ET SHELAH ⋮ Onn-dependent groups and fields ⋮ A CONJECTURAL CLASSIFICATION OF STRONGLY DEPENDENT FIELDS ⋮ Strongly dependent ordered abelian groups and Henselian fields ⋮ Onn-dependent groups and fields II ⋮ Groups and fields with $\operatorname {NTP}_{2}$ ⋮ DEFINABLE HENSELIAN VALUATIONS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Supersimplicity and quadratic extensions
• Generic structures and simple theories
• Supersimple fields and division rings
• Model theory of finite fields and pseudo-finite fields
• Abelian varieties over cyclic fields
• Notes on the stability of separably closed fields
• ELLIPTIC AND HYPERELLIPTIC CURVES OVER SUPERSIMPLE FIELDS
• The Theory of Ordered Abelian Groups does not have the Independence Property
• Additive Polynomials and Their Role in the Model Theory of Valued Fields
• Minimal bounded index subgroup for dependent theories
• Groups, measures, and the NIP
• Sous-groupes algébriques de rang maximum du groupe de Cremona
• Superstable fields and groups

This page was built for publication: Artin-Schreier extensions in NIP and simple fields