Submission date: 8 January 2022

Abstract:

Let K be a type-definable infinite field in an NIP theory. If K has characteristic p > 0, then K is Artin-Schreier closed (it has no Artin-Schreier extensions). As a consequence, p does not divide the degree of any finite separable extension of K. This generalizes a theorem of Kaplan, Scanlon, and Wagner.

Mathematics Subject Classification: 03C45, 03C60

Keywords and phrases:

Full text arXiv 2201.02778: pdf, ps.