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arXiv · 1501.04522

The existential theory of equicharacteristic henselian valued fields

Sylvy Anscombe·Arno Fehm
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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 $\mathbb{F}_{q}((t))$.

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Sylvy Anscombe, Arno Fehm. 2015-08-18. The existential theory of equicharacteristic henselian valued fields. https://doi.org/10.2140/ant.2016.10.665

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