The existential theory of equicharacteristic henselian valued fields
Sylvy Anscombe, Arno Fehm · Algebra & Number Theory · 2016
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 ކ q ((t)).