On dp-minimal fields

We classify dp-minimal pure fields up to elementary equivalence. Most are equivalent to Hahn series fields $K((t^Γ))$ where $Γ$ 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.

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