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On the cofinality of ultrapowers. (English) Zbl 0930.03060

Summary: 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.

MSC:

03E17 Cardinal characteristics of the continuum
03E05 Other combinatorial set theory
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