Vive la différence II. The Ax-Kochen isomorphism theorem |
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Authors: | Saharon Shelah |
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Institution: | (1) Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel;(2) Department of Mathematics, Rutgers University, New Brunswick, NJ, USA |
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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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