Blass, Andreas; Mildenberger, Heike On the cofinality of ultrapowers. (English) Zbl 0930.03060 J. Symb. Log. 64, No. 2, 727-736 (1999). 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. Cited in 17 Documents MathOverflow Questions: Is there any class of ideals for which \(\mathfrak{b}(\mathcal I)\neq\mathfrak{b}\)? MSC: 03E17 Cardinal characteristics of the continuum 03E05 Other combinatorial set theory Keywords:cofinalities of ultrapowers of the natural numbers; ultrafilters; cardinal characteristics of the continuum; splitting number; unsplitting number; groupwise density number; reduced powers; filters PDFBibTeX XMLCite \textit{A. Blass} and \textit{H. Mildenberger}, J. Symb. Log. 64, No. 2, 727--736 (1999; Zbl 0930.03060) Full Text: DOI arXiv Link References: [1] DOI: 10.1016/0168-0072(87)90082-0 · Zbl 0634.03047 · doi:10.1016/0168-0072(87)90082-0 [2] Set theory and its applications pp 18– (1989) [3] DOI: 10.1305/ndjfl/1093636772 · Zbl 0622.03040 · doi:10.1305/ndjfl/1093636772 [4] Open Problems in Topology pp 195– (1990) [5] DOI: 10.1016/0168-0072(88)90048-6 · Zbl 0646.03025 · doi:10.1016/0168-0072(88)90048-6 [6] DOI: 10.1007/BF01214984 · Zbl 0474.54003 · doi:10.1007/BF01214984 [7] Handbook of Set Theoretic Topology pp 111– (1984) [8] DOI: 10.1305/ndjfl/1093635237 · Zbl 0694.03029 · doi:10.1305/ndjfl/1093635237 [9] Czechoslovak Mathematical Journal 27 pp 556– (1977) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.