Journal of Symbolic Logic

More on regular reduced products

Juliette Cara Kennedy and Saharon Shelah

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Abstract

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

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

Dates
First available in Project Euclid: 2 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1102022222

Digital Object Identifier
doi:10.2178/jsl/1102022222

Mathematical Reviews number (MathSciNet)
MR1456106

Zentralblatt MATH identifier
1071.03033

Citation

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


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References

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