Eliminating field quantifiers in strongly dependent henselian fields

Halevi, Yatir; Hasson, Assaf

doi:10.1090/proc/14203

Eliminating field quantifiers in strongly dependent henselian fields
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by Yatir Halevi and Assaf Hasson PDF

Proc. Amer. Math. Soc. 147 (2019), 2213-2230 Request permission

Abstract:

We prove the 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.

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