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  1. The combinatorics of splittability.Boaz Tsaban - 2004 - Annals of Pure and Applied Logic 129 (1-3):107-130.
    Marion Scheepers, in his studies of the combinatorics of open covers, introduced the property asserting that a cover of type can be split into two covers of type . In the first part of this paper we give an almost complete classification of all properties of this form where and are significant families of covers which appear in the literature , using combinatorial characterizations of these properties in terms related to ultrafilters on . In the second part of the paper (...)
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  • Selective covering properties of product spaces.Arnold W. Miller, Boaz Tsaban & Lyubomyr Zdomskyy - 2014 - Annals of Pure and Applied Logic 165 (5):1034-1057.
    We study the preservation of selective covering properties, including classic ones introduced by Menger, Hurewicz, Rothberger, Gerlits and Nagy, and others, under products with some major families of concentrated sets of reals.Our methods include the projection method introduced by the authors in an earlier work, as well as several new methods. Some special consequences of our main results are : Every product of a concentrated space with a Hurewicz S1S1 space satisfies S1S1. On the other hand, assuming the Continuum Hypothesis, (...)
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