Viva la difference II. The Ax-Kochen isomorphism theorem

Details Viva la difference II. The Ax-Kochen isomorphism theorem Viva la difference II. The Ax-Kochen isomorphism theorem

1993-04-15

arxiv.org/abs/math/9304207v1

Israel J. Math. 85 (1994), 351--390

Mathematics

Logic

Scientific paper

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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