Submission date: 14 July 2015.

Abstract:

We show that dp-minimal valued fields are henselian and that a dp-minimal field admitting a definable type V topology is either real closed, algebraically closed or admits a non-trivial definable henselian valuation. We give classifications of dp-minimal ordered abelian groups and dp-minimal ordered fields without additional structure.

Mathematics Subject Classification: 03C45

Keywords and phrases:

Full text arXiv 1507.03911: pdf, ps.