Uniformly defining valuation rings in Henselian valued fields with finite or pseudo-finite residue fields

DOI10.1016/J.APAL.2013.06.010zbMath1370.11138arXiv1306.1802OpenAlexW1970664562MaRDI QIDQ490661

Jamshid Derakhshan, Eva Leenknegt, Raf Cluckers, Angus J. Macintyre

Publication date: 27 August 2015

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.1802

zbMATH Keywords

definabilityDiophantine setsHilbert's tenth problem

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Model-theoretic algebra (03C60) Model theory (number-theoretic aspects) (11U09) (p)-adic and power series fields (11D88)

Related Items (14)

On the quantifier complexity of definable canonical Henselian valuations ⋮ A definable Henselian valuation with high quantifier complexity ⋮ Some supplements to Feferman-Vaught related to the model theory of adeles ⋮ Between the Rings $${\mathbb Z}/p^n{\mathbb Z}$$ and the Ring $${\mathbb Z}_p$$: Issues of Axiomatizability, Definability and Decidability ⋮ Decidability of the class of all the rings : A problem of Ax ⋮ Definable Valuations Induced by Definable Subgroups ⋮ Recent progress on definability of Henselian valuations ⋮ AN EXISTENTIAL ∅-DEFINITION OF IN ⋮ DEFINABLE HENSELIAN VALUATION RINGS ⋮ Model theory of adeles. I. ⋮ Uniform definability of henselian valuation rings in the Macintyre language: ⋮ DEFINABLE HENSELIAN VALUATIONS ⋮ EXISTENTIAL ∅-DEFINABILITY OF HENSELIAN VALUATION RINGS ⋮ An undecidability result for the asymptotic theory of \(p\)-adic fields

This page was built for publication: Uniformly defining valuation rings in Henselian valued fields with finite or pseudo-finite residue fields