Eliminating field quantifiers in strongly dependent henselian fields

Yatir Halevi; Assaf Hasson; Heike Mildenberger

doi:10.1090/proc/14203

Eliminating field quantifiers in strongly dependent henselian fields

Yatir Halevi, Assaf Hasson, Heike Mildenberger

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

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.

Original language	English
Pages (from-to)	2213-2230
Number of pages	18
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	5
DOIs	https://doi.org/10.1090/proc/14203
State	Published - 1 May 2019

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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title = "Eliminating field quantifiers in strongly dependent henselian fields",

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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N2 - 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.

AB - 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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Eliminating field quantifiers in strongly dependent henselian fields

Abstract

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