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Dec 20, 2020 at 22:51 history edited YCor CC BY-SA 4.0
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Dec 20, 2020 at 22:00 comment added Erik Walsberg thanks, I will add this to my answer.
Dec 20, 2020 at 22:00 history edited Erik Walsberg CC BY-SA 4.0
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Dec 20, 2020 at 7:06 comment added Arno Fehm The paper "Slim fields" by Junker and Koenigsmann might be of interest here. In particular they show that both perfect PAC fields and henselian fields of characteristic zero are "very slim", in particular they have no definable infinite subfields.
Dec 20, 2020 at 3:57 vote accept Keshav Srinivasan
Dec 20, 2020 at 3:55 history answered Erik Walsberg CC BY-SA 4.0