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Jan 25, 2021 at 0:04 history edited Wojowu CC BY-SA 4.0
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Jan 25, 2021 at 0:00 comment added Wojowu @AndreasBlass That's a good point, thank you. I'll add it to the answer.
Jan 24, 2021 at 23:53 comment added Andreas Blass About the last sentence of the answer: If $U$ is countably complete, and $E,F$ are countable, then the ultrapowers by $U$ are canonically isomorphic to $E,F$ themselves, so the Galois group doesn't change. The same is true if the cardinalities of $E,F$ are uncountable but smaller than the first measurable cardinal.
Jan 24, 2021 at 23:27 vote accept Keshav Srinivasan
Jan 24, 2021 at 22:59 history answered Wojowu CC BY-SA 4.0