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On the size of closed unbounded sets. (English) Zbl 0746.03040

The problem of determining the size of the closed unbounded subsets of \([\lambda]^{<\kappa}\) is reduced to the study of certain stationary sets and further related to combinatorial principles \(Q_ 1\) and \(Q_ 2\) and the notion of \(\alpha\)-remarkable cardinals (a weakening of \(\alpha\)-Erdős). Consistency and independence results are obtained connecting these principles to Jensen’s \(\square\)-principles.

MSC:

03E05 Other combinatorial set theory
03E35 Consistency and independence results
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