Submission date: 9 July 2015.

Abstract:

We classify dp-minimal pure fields up to elementary equivalence. Most are equivalent to Hahn series fields K((t^Γ)) where Γ satisfies some divisibility conditions and K is 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.

Mathematics Subject Classification: 03C45

Keywords and phrases:

Full text arXiv 1507.02745: pdf, ps.