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On the cofinality of ultrapowers

Published online by Cambridge University Press:  12 March 2014

Andreas Blass  and
Heike Mildenberger
Andreas Blass
Affiliation:
Mathematics Department, University of Michigan, Ann Arbor, MI 48109, U.S.A. E-mail: ablass@umich.edu
Heike Mildenberger
Affiliation:
Mathematisches Institut der Universität Bonn, Beringstrasse 1, 53115 Bonn, Germany E-mail: heike@math.uni-bonn.de
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Abstract

We prove some restrictions on the possible cofinalities of ultrapowers of the natural numbers with respect to ultrafilters on the natural numbers. The restrictions involve three cardinal characteristics of the continuum, the splitting number s, the unsplitting number r, and the groupwise density number g. We also prove some related results for reduced powers with respect to filters other than ultrafilters.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 2 , June 1999 , pp. 727 - 736
Copyright
Copyright © Association for Symbolic Logic 1999

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References

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