Cummings, James; Shelah, Saharon Cardinal invariants above the continuum. (English) Zbl 0835.03013 Ann. Pure Appl. Logic 75, No. 3, 251-268 (1995). Summary: We prove some consistency results about \({\mathfrak b} (\lambda)\) and \({\mathfrak d} (\lambda)\), which are natural generalisations of the cardinal invariants of the continuum \({\mathfrak b}\) and \({\mathfrak d}\). We also define invariants \({\mathfrak b}_{\text{cl}} (\lambda)\) and \({\mathfrak d}_{\text{cl}} (\lambda)\), and prove that almost always \({\mathfrak b} (\lambda) = {\mathfrak b}_{\text{cl}} (\lambda)\) and \({\mathfrak d} (\lambda) = {\mathfrak d}_{\text{cl}} (\lambda)\). Cited in 30 Documents MSC: 03E35 Consistency and independence results Keywords:consistency; cardinal invariants PDFBibTeX XMLCite \textit{J. Cummings} and \textit{S. Shelah}, Ann. Pure Appl. Logic 75, No. 3, 251--268 (1995; Zbl 0835.03013) Full Text: DOI arXiv References: [1] Baumgartner, J. E., Iterated forcing, (Mathias, A., Surveys in Set Theory. Surveys in Set Theory, LMS Lecture Notes, 87 (1983), Cambridge Univ. Press: Cambridge Univ. Press Cambridge), 1-59 · Zbl 0524.03040 [2] van Douwen, E. K., The integers and topology, (Kunen, K.; Vaughan, J. E., Handbook of Set-Theoretic Topology (1984), North-Holland: North-Holland Amsterdam), 111-167 [3] Easton, W., Powers of regular cardinals, Ann. Math. Logic, 1, 139-178 (1964) · Zbl 0209.30601 [4] Hechler, S., On the existence of certain cofinal subsets of \(ω^ω\), Axiomatic Set Theory, (Proceedings of Symposia in Pure Mathematics, Vol. 13 (1974), Amer. Mathematical Soc: Amer. Mathematical Soc Providence, RI), 155-173, Part II [5] Magidor, M.; Shelah, S., When does almost free imply free?, J. Amer. Math. Soc., 7, 769-830 (1994) · Zbl 0819.20059 [6] S. Shelah, The generalised continuum hypothesis revisited, Israel J. Math., to appear.; S. Shelah, The generalised continuum hypothesis revisited, Israel J. Math., to appear. · Zbl 0955.03054 [7] J. Zapletal, Splitting number and the core model, to appear.; J. Zapletal, Splitting number and the core model, to appear. 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.