Covering the Baire space by families which are not finitely dominating

DOI10.1016/j.apal.2005.09.008zbMath1098.03056arXivmath/0407487OpenAlexW2116747822MaRDI QIDQ2493904

Saharon Shelah, Heike Mildenberger, Boaz Tsaban

Publication date: 16 June 2006

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0407487

zbMATH Keywords

cofinality of ultrapowersfinitely dominating familiesgroupwise density number \(\mathfrak g\)unbounding number \(\mathfrak b\)

Mathematics Subject Classification ID

Descriptive set theory (03E15) Consistency and independence results (03E35) Cardinal characteristics of the continuum (03E17) Higher-type and set recursion theory (03D65)

Related Items (6)

Selective covering properties of product spaces ⋮ Exactly two and exactly three near-coherence classes ⋮ On the length of chains of proper subgroups covering a topological group ⋮ The cofinality of the symmetric group and the cofinality of ultrapowers ⋮ The near coherence of filters principle does not imply the filter dichotomy principle ⋮ Combinatorial images of sets of reals and semifilter trichotomy

Cites Work

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• Maximal chains in \(^ \omega \omega\) and ultrapowers of the integers
• There may be simple \(P_{\aleph _ 1}\)- and \(P_{\aleph _ 2}\)-points and the Rudin-Keisler ordering may be downward directed
• Combinatorial Cardinal Characteristics of the Continuum
• Models in Which Every Nonmeager Set is Nonmeager in a Nowhere Dense Cantor Set
• Critical Cardinalities and Additivity Properties of Combinatorial Notions of Smallness
• Groupwise dense families

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