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More on regular reduced products

Published online by Cambridge University Press:  12 March 2014

Juliette Cara Kennedy
Department of Mathematics and Statistics, P.O. Box 68 (Gustaf Hällströmin Katu 2B), FI-00014, University of Helsinki, Finland, E-mail:
Saharon Shelah
Institute of Mathematics, Hebrew University, Jerusalem, Israel, E-mail:


The authors show, by means of a finitary version of the combinatorial principle 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 ΠiMi/D and ΠiNi/D. If in addition 2λ = λ+ and i < λ implies |Mi| + |Ni| ≤ λ+ this means that the ultrapowers are isomorphic. This settles negatively conjecture 18 in [2].

Research Article
Copyright © Association for Symbolic Logic 2004

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