English

Type-definable NIP fields are Artin-Schreier closed

Logic 2022-01-11 v1

Abstract

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

Keywords

Cite

@article{arxiv.2201.02778,
  title  = {Type-definable NIP fields are Artin-Schreier closed},
  author = {Will Johnson},
  journal= {arXiv preprint arXiv:2201.02778},
  year   = {2022}
}

Comments

11 pages

R2 v1 2026-06-24T08:43:32.647Z