Journal of Symbolic Logic

More on regular reduced products

Juliette Cara Kennedy and Saharon Shelah

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


The authors show, by means of a finitary version □finλ, D of the combinatorial principle □b*λ of [7], the consistency of the failure, relative to the consistency of supercompact cardinals, of the following: for all regular filters D on a cardinal λ, if Mi and Ni are elementarily equivalent models of a language of size ≤ λ, then the second player has a winning strategy in the Ehrenfeucht-Fraïssé game of length λ+ on ∏i Mi/D and ∏i Ni/D. If in addition 2λ+ and i <λ implies |Mi|+|Ni|≤ λ+ this means that the ultrapowers are isomorphic. This settles negatively conjecture 18 in [2].

Article information

J. Symbolic Logic, Volume 69, Issue 4 (2004), 1261-1266.

First available in Project Euclid: 2 December 2004

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Kennedy, JulietteCara; Shelah, Saharon. More on regular reduced products. J. Symbolic Logic 69 (2004), no. 4, 1261--1266. doi:10.2178/jsl/1102022222.

Export citation


  • S. Ben-David On Shelah's compactness of cardinals, Israel Journal of Mathematics, vol. 31 (1978), pp. 34--56.
  • C. C. Chang and J. Keisler Model theory, North-Holland,1990.
  • J. Keisler Ultraproducts and saturated models, Koninklijke Nederlandse Akademie van Wetenschappen. Proceedings Series A, vol. 67 (1964), pp. 178--186, ($=$ Indagationes Mathematicae. New Series, vol. 26).
  • J. Kennedy and S. Shelah On regular reduced products, Journal of Symbolic Logic, vol. 67 (2002), pp. 1169--1177.
  • S. Shelah Every two elementarily equivalent models have isomorphic ultrapowers, Israel Journal of Mathematics, vol. 10 (1971), pp. 224--233.