Vive La Différence Iii

Vive la différence II. The Ax-Kochen isomorphism theorem

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 [...

Vive la Différence I: Nonisomorphism of ultrapowers of countable models

We show that it is not provable in ZFC that any two countable elementarily equivalent structures have isomorphic ultrapowers relative to some ultrafilter on ω. The author thanks the BSF and the Basic Research Fund, Israeli Academy of Sciences and the NSF for partial support of this research. This paper owes its existence to Annalisa Marcja’s hospitality in Trento, July 1987; van den Dries’ curi...

Vive la science! Vive le hérisson!

The EMBO workshop 'Hedgehog Signalling: from Developmental Biology to Anti-cancer Drugs' took place between 27 and 31 March on the beautiful Côte d'Azur. The gathered scientists tackled topics ranging from the mechanisms by which Hedgehog (Hh) is presented to receptive cells, to the distribution of Hh by Glypicans, to the role of cilia in vertebrate Hh signal transduction, and to the function o...

The Nutrition Society journals: vive la différence!

Vive la résistance!

In vitro evolution experiments reveal that single mutations in three genes can increase the ability of E. coli to survive ionizing radiation by a factor of 1000.