On dp-minimal fields

Will Johnson

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arXiv · 1507.02745

On dp-minimal fields

Will Johnson

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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.

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Will Johnson. 2015-07-09. On dp-minimal fields. https://arxiv.org/abs/1507.02745

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