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Cardinal invariants above the continuum. (English) Zbl 0835.03013

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 \({\mathfrak d} (\lambda) = {\mathfrak d}_{\text{cl}} (\lambda)\).

MSC:

03E35 Consistency and independence results
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