Journal of Symbolic Logic

Regular ultrafilters and finite square principles

Juliette Kennedy, Saharon Shelah, and Jouko Väänänen

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We show that many singular cardinals λ above a strongly compact cardinal have regular ultrafilters D that violate the finite square principle □finλ,D introduced in [3]. For such ultrafilters D and cardinals λ there are models of size λ for which Mλ/D is not λ++-universal and elementarily equivalent models M and N of size λ for which Mλ/D and Nλ/D are non-isomorphic. The question of the existence of such ultrafilters and models was raised in [1].

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J. Symbolic Logic, Volume 73, Issue 3 (2008), 817-823.

First available in Project Euclid: 27 December 2008

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Kennedy, Juliette; Shelah, Saharon; Väänänen, Jouko. Regular ultrafilters and finite square principles. J. Symbolic Logic 73 (2008), no. 3, 817--823. doi:10.2178/jsl/1230396748.

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