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2016 The existential theory of equicharacteristic henselian valued fields
Sylvy Anscombe, Arno Fehm
Algebra Number Theory 10(3): 665-683 (2016). DOI: 10.2140/ant.2016.10.665

Abstract

We study the existential (and parts of the universal-existential) theory of equicharacteristic henselian valued fields. We prove, among other things, an existential Ax–Kochen–Ershov principle, which roughly says that the existential theory of an equicharacteristic henselian valued field (of arbitrary characteristic) is determined by the existential theory of the residue field; in particular, it is independent of the value group. As an immediate corollary, we get an unconditional proof of the decidability of the existential theory of Fq((t)).

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Sylvy Anscombe. Arno Fehm. "The existential theory of equicharacteristic henselian valued fields." Algebra Number Theory 10 (3) 665 - 683, 2016. https://doi.org/10.2140/ant.2016.10.665

Information

Received: 18 September 2015; Revised: 9 February 2016; Accepted: 15 March 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1377.03025
MathSciNet: MR3513134
Digital Object Identifier: 10.2140/ant.2016.10.665

Subjects:
Primary: 03C60
Secondary: 11U05, 12J10, 12L05, 12L12

Rights: Copyright © 2016 Mathematical Sciences Publishers

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Vol.10 • No. 3 • 2016
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