Zdomsky, Lubomyr A semifilter approach to selection principles. (English) Zbl 1121.03060 Commentat. Math. Univ. Carol. 46, No. 3, 525-539 (2005). Summary: In this paper we develop the semifilter approach to the classical Menger and Hurewicz properties and show that the small cardinal \(\mathfrak g\) is a lower bound of the additivity number of the \(\sigma \)-ideal generated by Menger subspaces of the Baire space, and under \(\mathfrak u < \mathfrak g\) every subset \(X\) of the real line with the property \(\text{Split} (\Lambda ,\Lambda )\) is Hurewicz, and thus it is consistent with ZFC that the property \(\text{Split} (\Lambda ,\Lambda )\) is preserved by unions of less than \(\mathfrak b\) subsets of the real line. Cited in 1 ReviewCited in 20 Documents MSC: 03E17 Cardinal characteristics of the continuum 03E35 Consistency and independence results 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.) Keywords:Menger property; Hurewicz property PDFBibTeX XMLCite \textit{L. Zdomsky}, Commentat. Math. Univ. Carol. 46, No. 3, 525--539 (2005; Zbl 1121.03060) Full Text: arXiv EuDML EMIS