More on Regular Reduced Products

Journal of Symbolic Logic 69 (4):1261 - 1266 (2004)
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Abstract

The authors show. by means of a finitary version $\square_{\lambda D}^{fin}$ of the combinatorial principle $\square_\lambda^{h*}$ 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 A. if Mi and Ni are elementarily equivalent models of a language of size $\leq \lambda$ , then the second player has a winning strategy in the Ehrenfeucht- $Fra\uml{i}ss\acute{e}$ game of length $\lambda^{+}$ on $\pi_{i} M_{i}/D$ and $\pi_{i} N_{i}/D$ . If in addition $2^{\lambda} = \labda^{+}$ and i < $\lambda$ implies | $M_{i}$ | +| $N_{i}$ | $\leq$ \lambda^{+} this means that the ultrapowers are isomorphic. This settles negatively conjecture 18 in [2]

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Author's Profile

Juliette Cara Kennedy
University of Helsinki

Citations of this work

Regular Ultrapowers at Regular Cardinals.Juliette Kennedy, Saharon Shelah & Jouko Väänänen - 2015 - Notre Dame Journal of Formal Logic 56 (3):417-428.
Atomic Saturation of Reduced Powers.Saharon Shelah - forthcoming - Mathematical Logic Quarterly.

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References found in this work

Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.

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