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arXiv · 1307.8004

On VC-minimal fields and dp-smallness

Vincent Guingona
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Abstract

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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Vincent Guingona. 2013-07-30. On VC-minimal fields and dp-smallness. https://arxiv.org/abs/1307.8004

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