[FOM] Shipman's field question
JoeShipman at aol.com
Thu Oct 26 10:23:32 EDT 2006
>From: marker at math.uic.edu
>To say a bit more about your original question.
>Tom Scanlon (building on work of Pop, Poonen and others) has
>recently proved that if K is a finitely generated field, there is a
>sentence describing K up to isomorphism among the finitely generated
>fields. In particular, this proves Pop's conjecture that elementarily
>equivalent finitely generated fields are isomorphic.
That's great, just the result I need.
Can there be two nonisomorphic countable fields which have the same
finitely generated subfields? (This question is slightly imprecise,
because an easy way out would be if they have the same isomorphism
classes of finitely generated subfields but different numbers of some
given isomorphism class, if there is such an easy way out modify my
question in the obvious way).
Is the answer different for char 0 and positive characteristic? (In positive
characteristic I can see non-separability creating difficulties....)
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