Existentially generated subfields of large fields

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 \subseteq 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.