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In this paper, we show that VC-minimal ordered fields are real closed. We introduce a notion, strictly between convexly orderable and dp-minimal, that we call dp-small, and show that this is enough to characterize many algebraic theories. For example, dp-small ordered groups are abelian divisible and dp-small ordered fields are real closed.

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Correspondence to Vincent Guingona.

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The author was supported by NSF Grant DMS-0838506.

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Guingona, V. On VC-minimal fields and dp-smallness. Arch. Math. Logic 53, 503–517 (2014).

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Mathematics Subject Classification (2010)