On dp-minimal fields

Abstract

We classify dp-minimal pure fields up to elementary equivalence. Most are equivalent to Hahn series fields $K((t^{\Gamma }))$ where $\Gamma$ satisfies some divisibility conditions and $K$ is ${\mathbb{F}}_p^{alg}$ or a local field of characteristic zero. We show that dp-small fields (including VC-minimal fields) are algebraically closed or real closed.

32 pages

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• Dp-finite fields V: topological fields of finite weight
• On Strongly NIP Ordered Fields and Definable Convex Valuations
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• Notes on trace equivalence