Eliminating Field Quantifiers in Strongly Dependent Henselian Fields

Abstract

We prove elimination of field quantifiers for strongly dependent henselian fields in the Denef-Pas language. This is achieved by proving the result for a class of fields generalizing algebraically maximal Kaplansky fields. We deduce that if $(K,v)$ is strongly dependent then so is its henselization.

arXiv commentThe original version was for algebraically maximal kaplansky fields. This new version is a generalization