Eliminating Field Quantifiers in Strongly Dependent Henselian Fields
Yatir Halevi, Assaf Hasson · arXiv (Cornell University) · 2017
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.