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(pn), the pn-th powers in L, for some n<ω. This generalises a result of Fehm from [4], 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.

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