Definable Valuations induced by multiplicative subgroups and NIP Fields

2017/04/10 by Dupont, Katharina, Hasson, Assaf, Kuhlmann, Salma · 2 citations
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1704.02910

Abstract

We study the algebraic implications of the non-independence property (NIP) and variants thereof (dp-minimality) on infinite fields, motivated by the conjecture that all such fields which are neither real closed nor separably closed admit a definable henselian valuation. Our results mainly focus on Hahn fields and build up on Will Johnson's preprint "dp-minimal fields", arXiv: 1507.02745v1, July 2015.

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