On dp-minimal fields

2015/07/09 by Johnson, Will
#03C45 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1507.02745

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 \mathbbF_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.

Related

• On VC-minimal fields and dp-smallness
• Dp-minimal valued fields
• Definable henselian valuations on dp-minimal real fields
• Definable completeness of P-minimal fields and applications
• Dp-finite fields I: infinitesimals and positive characteristic