Characterizing NIP henselian fields

Abstract

In this paper, we characterize NIP henselian valued fields modulo the theory of their residue field, both in an algebraic and in a model-theoretic way. Assuming the conjecture that every infinite NIP field is either separably closed, real closed or admits a non-trivial henselian valuation, this allows us to obtain a characterization of all theories of NIP fields.

18 pages

References in corpus (3)

• The étale-open topology and the stable fields conjecture
• Dp-finite fields I: infinitesimals and positive characteristic
• Ax-Kochen-Ershov principles for finitely ramified henselian fields

Cited by in corpus (3)

• Dp-finite fields V: topological fields of finite weight
• Definable henselian valuations in positive residue characteristic
• Artin-Schreier extensions and combinatorial complexity in henselian valued fields