#### Vol. 10, No. 3, 2016

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editors' Addresses Editors' Interests Scientific Advantages Submission Guidelines Submission Form Editorial Login Ethics Statement Author Index To Appear ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Other MSP Journals
The existential theory of equicharacteristic henselian valued fields

### Sylvy Anscombe and Arno Fehm

Vol. 10 (2016), No. 3, 665–683
##### 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 ${\mathbb{F}}_{q}\left(\left(t\right)\right)$.

##### Keywords
model theory, henselian valued fields, decidability, diophantine equations
##### Mathematical Subject Classification 2010
Primary: 03C60
Secondary: 12L12, 12J10, 11U05, 12L05