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December 2004 More on regular reduced products
Juliette Cara Kennedy, Saharon Shelah
J. Symbolic Logic 69(4): 1261-1266 (December 2004). DOI: 10.2178/jsl/1102022222

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].

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Juliette Cara Kennedy. Saharon Shelah. "More on regular reduced products." J. Symbolic Logic 69 (4) 1261 - 1266, December 2004. https://doi.org/10.2178/jsl/1102022222

Information

Published: December 2004
First available in Project Euclid: 2 December 2004

zbMATH: 1071.03033
MathSciNet: MR1456106
Digital Object Identifier: 10.2178/jsl/1102022222

Rights: Copyright © 2004 Association for Symbolic Logic

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Vol.69 • No. 4 • December 2004
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