Title

Characterizing NIP henselian valued fields

Abstract

In this talk we characterize NIP henselian valued fields modulo the theory of their residue field. In particular, we show that every NIP henselian valued field satisfies some instance of the Ax-Kochen/Ersov principle. We then discuss several consequences of the theorem, including a characterization of all NIP fields when one assumes the conjecture that every infinite NIP field is either separably closed, real closed or admits a henselian valuation. We also discuss open questions arising from these results. This is joint work with Sylvy Anscombe.

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