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Regular ultrafilters and finite square principles

Published online by Cambridge University Press:  12 March 2014

Juliette Kennedy ,
Saharon Shelah  and
Jouko Väänänen
Juliette Kennedy
Affiliation:
Department of Philosophy, Utrecht University, Netherlands Department of Mathematics and Statistics, University of Helsinki, Finland, E-mail: jkennedy@cc.helsinki.fi
Saharon Shelah
Affiliation:
Department of Philosophy, Utrecht University, Netherlands Institute of Mathematics, Hebrew University, Jerusalem, Israel, E-mail: shelah@math.huji.ac.il
Jouko Väänänen
Affiliation:
Department of Philosophy, Utrecht University, Netherlands Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, Netherlands, E-mail: jouko.vaananen@helsinki.fi
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Abstract

We show that many singular cardinals λ above a strongly compact cardinal have regular ultrafilters D that violate the finite square principle 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].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 3 , September 2008 , pp. 817 - 823
Copyright
Copyright © Association for Symbolic Logic 2008

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References

REFERENCES

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