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Feb 18, 2012 at 3:31 comment added Yemon Choi Jon, I must confess that I don't know how Gromov's proof works, but given that one can define and investigate sofic groups in terms of embeddings into suitable ultrapowers, your suggestion sounds very plausible.
Feb 17, 2012 at 23:45 comment added Jon Bannon This is a good one. Isn't Gromov's partial solution an extension of Ax-Grothendieck to some sort of "limit varieties"?
Feb 17, 2012 at 22:19 history answered Yemon Choi CC BY-SA 3.0