Several comments about the combinatorics of τ-cover


In a previous work with Mildenberger and Shelah, we showed that the combinatorics of the selection hypotheses involving τ-covers is sensitive to the selection operator used. We introduce a natural generalization of Scheepers’ selection operators, and show that: (1) A slight change in the selection operator, which in classical cases makes no difference,leads to different properties when τ-covers are involved. (2) One of the newly introduced properties sheds some light on a problem of Scheepers concerning τ-covers. Improving an earlier result, we also show that no generalized Luzin set satisfies Ufin(Γ,τ)

DOI Code: 10.1285/i15900932v27supn1p47

Keywords: Combinatorial cardinal characteristics of the continuum; γ-cover; ω-cover; τ-cover; Selection principles; Borel covers; Open cover

Classification: 03E05; 54D20; 54D80

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