Submission date: 11 July 2016

Abstract:

Let K be an NIP field and let v be a henselian valuation on K. We ask whether (K,v) is NIP as a valued field. By a result of Shelah, we know that if v is externally definable, then (K,v) is NIP. Using the definability of the canonical p-henselian valuation, we show that whenever the residue field of v is not separably closed, then v is externally definable. We also give a weaker statement for the case of separably closed residue fields.

Mathematics Subject Classification: 03C45, 12L12

Keywords and phrases:

Full text arXiv 1607.02953: pdf, ps.