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).
Original language | French |
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Pages (from-to) | 351-390 |
Number of pages | 40 |
Journal | Israel Journal of Mathematics |
Volume | 85 |
Issue number | 1-3 |
DOIs | |
State | Published - Feb 1994 |