### Vive la diff\'erence II. The Ax-Kochen isomorphism theorem

by Shelah. [Sh:405]

Israel J Math, 1994

We show in section 1 that the Ax-Kochen isomorphism theorem requires
the continuum hypothesis. Most of the applications of this theorem
are insensitive to set theoretic considerations. (A probable
exception is the work of Moloney.) In section 2 we give an unrelated
result on cuts in models of Peano arithmetic which answers a
question on the ideal structure of countable ultraproducts of
Z . In section 1 we also answer a question of Keisler and Schmerl
regarding Scott complete ultrapowers of R .

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