Point-cofinite covers in the laver model

Arnold W. Miller, Boaz Tsaban

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Let S1(Γ, Γ) be the statement: For each sequence of point-cofinite open covers, one can pick one element from each cover and obtain a point-cofinite cover. b is the minimal cardinality of a set of reals not satisfying S1(Γ, Γ). We prove the following assertions: (1) If there is an unbounded tower, then there are sets of reals of cardinality b satisfying S1(Γ, Γ). (2) It is consistent that all sets of reals satisfying S1(Γ, Γ) have cardinality smaller than b. These results can also be formulated as dealing with Arhangel'skiǐ's property α2 for spaces of continuous real-valued functions. The main technical result is that in Laver's model, each set of reals of cardinality b has an unbounded Borel image in the Baire space ωω.

Original languageEnglish
Pages (from-to)3313-3321
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number9
StatePublished - Sep 2010


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