The ultraproduct of all finite prime fields $ \Bbb F_p $ (over a nonprincipal ultrafilter U) is a field of characteristic 0. How do I show that it has exactly one extension of degree n for each natural number n?
2026-04-07 03:35:53.1775532953
Field extensions of $\prod \Bbb F_p /U$
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Hint: First show that this is true for all of the fields $\mathbb{F}_p$.
Then (Harder) try to express this in a first-order way.