Submission date: 30 July 2013.

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.

Mathematics Subject Classification: 03C60, 03C45, 12J15

Keywords and phrases:

Full text arXiv 1307.8004: pdf, ps.