Quantifier elimination for Henselian fields relative to additive and multiplicative congruences

DOI10.1007/BF02758645zbMath0809.03028OpenAlexW1977994178MaRDI QIDQ1320036

Franz-Viktor Kuhlmann

Publication date: 19 April 1994

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

Full work available at URL: https://doi.org/10.1007/bf02758645

zbMATH Keywords

Henselian fieldsvalued fields

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Model theory of fields (12L12) Quantifier elimination, model completeness, and related topics (03C10) Valued fields (12J10) Formally (p)-adic fields (12J12)

Related Items

The algebra and model theory of tame valued fields, NOTES ON EXTREMAL AND TAME VALUED FIELDS, Some supplements to Feferman-Vaught related to the model theory of adeles, Mini-workshop: Topological and differential expansions of o-minimal structures. Abstracts from the mini-workshop held November 27 -- December 3, 2022, Elimination of imaginaries in C((Γ))$\mathbb {C}((\Gamma ))$, The classification of dp-minimal and dp-small fields, Eliminating field quantifiers in strongly dependent henselian fields, SOME PROPERTIES OF ANALYTIC DIFFERENCE VALUED FIELDS, An isomorphism theorem for Henselian algebraic extensions of valued fields, Hyperfields, truncated DVRs, and valued fields, A P-MINIMAL STRUCTURE WITHOUT DEFINABLE SKOLEM FUNCTIONS, Model theory of adeles. I., Strongly dependent ordered abelian groups and Henselian fields, A closedness theorem over Henselian fields with analytic structure and its applications, Relative decidability and definability in henselian valued fields, Analytic cell decomposition and analytic motivic integration, Diophantine problems over tamely ramified fields, Cell decomposition and definable functions for weakp-adic structures

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Complete theories
• Relative elimination of quantifiers for Henselian valued fields
• Dimension of definable sets, algebraic boundedness and Henselian fields
• Formally \(p\)-adic fields
• Immediate and purely wild extensions of valued fields
• An isomorphism theorem for Henselian algebraic extensions of valued fields
• Model theory
• Elementary Properties of Ordered Abelian Groups
• On definable subsets of p-adic fields