## Algebra & Number Theory

### The existential theory of equicharacteristic henselian valued fields

#### 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 $Fq((t))$.

#### Article information

Source
Algebra Number Theory, Volume 10, Number 3 (2016), 665-683.

Dates
Revised: 9 February 2016
Accepted: 15 March 2016
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.ant/1510842499

Digital Object Identifier
doi:10.2140/ant.2016.10.665

Mathematical Reviews number (MathSciNet)
MR3513134

Zentralblatt MATH identifier
1377.03025

#### Citation

Anscombe, Sylvy; Fehm, Arno. The existential theory of equicharacteristic henselian valued fields. Algebra Number Theory 10 (2016), no. 3, 665--683. doi:10.2140/ant.2016.10.665. https://projecteuclid.org/euclid.ant/1510842499

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