Type-definable NIP fields are Artin-Schreier closed
Logic
2022-01-11 v1
Abstract
Let be a type-definable infinite field in an NIP theory. If has characteristic , then is Artin-Schreier closed (it has no Artin-Schreier extensions). As a consequence, does not divide the degree of any finite separable extension of . 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