Submission date: 9 October 2017

Abstract:

We study subfields of large fields which are generated by infinite existentially definable subsets. We say that such subfields are existentially generated. Let L be a large field of characteristic exponent p, and let E⊆ L be an infinite existentially generated subfield. We show that E contains L^{(p^{n})}, the p^{n}-th powers in L, for some n< ω. This generalises a result of Fehm, which shows E=L under the assumption that L is perfect. Our method is to first study existentially generated subfields of henselian fields. Since L is existentially closed in the henselian field L((t)), our result follows.

Mathematics Subject Classification: 11U09, 03C60, 12J10

Keywords and phrases:

Full text arXiv 1710.03353: pdf, ps.