Journal of Symbolic Logic

On the Cofinality of Ultrapowers

Andreas Blass and Heike Mildenberger

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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 $\mathfrak{s}$, the unsplitting number $\mathfrak{r}$, and the groupwise density number $\mathfrak{g}$. We also prove some related results for reduced powers with respect to filters other than ultrafilters.

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J. Symbolic Logic, Volume 64, Issue 2 (1999), 727-736.

First available in Project Euclid: 6 July 2007

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Blass, Andreas; Mildenberger, Heike. On the Cofinality of Ultrapowers. J. Symbolic Logic 64 (1999), no. 2, 727--736.

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