Existential 0-definability of henselian valuation rings

TL;DR

This paper extends existing methods to establish existential 0-definability of valuation rings in henselian valued fields with finite or pseudo-algebraically closed residue fields, broadening the scope of definability results.

Contribution

It generalizes previous definability results by applying the method to a wider class of henselian valued fields with various residue fields.

Findings

Existential 0-definability of valuation rings in broader henselian fields.

Extension of methods from finite residue fields to pseudo-algebraically closed fields.

New definability results applicable to a wider class of valued fields.

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.