# Sh:405

- Shelah, S. (1994).
*Vive la différence. II. The Ax-Kochen isomorphism theorem*. Israel J. Math.,**85**(1-3), 351–390. arXiv: math/9304207 DOI: 10.1007/BF02758648 MR: 1264351 -
Abstract:

We show in §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 §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 {\mathbb Z}. In §1 we also answer a question of Keisler and Schmerl regarding Scott complete ultrapowers of {\mathbb R}. - Version 2021-07-20 (33p) published version (40p)

Bib entry

@article{Sh:405, author = {Shelah, Saharon}, title = {{Vive la diff\'erence. II. The Ax-Kochen isomorphism theorem}}, journal = {Israel J. Math.}, fjournal = {Israel Journal of Mathematics}, volume = {85}, number = {1-3}, year = {1994}, pages = {351--390}, issn = {0021-2172}, mrnumber = {1264351}, mrclass = {03C20 (03C62 03E35 03H15 12L10 12L15)}, doi = {10.1007/BF02758648}, note = {\href{https://arxiv.org/abs/math/9304207}{arXiv: math/9304207}}, arxiv_number = {math/9304207} }