Abstract
We show in §1 that the Ax-Kochen isomorphism theorem [AK] 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 [Mo].) In §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 posed in [LLS]. In §1 we also answer a question of Keisler regarding Scott complete ultrapowers of ℝ (see 1.18).
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Shelah, S. Vive la différence II. The Ax-Kochen isomorphism theorem. Israel J. Math. 85, 351–390 (1994). https://doi.org/10.1007/BF02758648
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DOI: https://doi.org/10.1007/BF02758648