Existential 0-definability of henselian valuation rings

Abstract

Recently, Anscombe and Koenigsmann gave an existential 0-definition of the ring of formal power series F[[t]] in its quotient field in the case where F is finite. We extend their method in several directions to give general definability results for henselian valued fields with finite or pseudo-algebraically closed residue fields.

minor corrections, Theorem 4.1 strengthened, Remark 4.2 added

References in corpus (2)

• An existential 0-definition of F_q[[t]] in F_q((t))
• Uniformly defining valuation rings in Henselian valued fields with finite or pseudo-finite residue fields

Cited by in corpus (1)

• Definable henselian valuations