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  1.  26 DLs
    Tomek Bartoszynski, Saharon Shelah & Boaz Tsaban (2003). Additivity Properties of Topological Diagonalizations. Journal of Symbolic Logic 68 (4):1254-1260.
    We answer a question of Just, Miller, Scheepers and Szeptycki whether certain diagonalization properties for sequences of open covers are provably closed under taking finite or countable unions.
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  2.  2 DLs
    Boaz Tsaban & Lyubomyr Zdomskyy (2006). Menger's Covering Property and Groupwise Density. Journal of Symbolic Logic 71 (3):1053 - 1056.
    We establish a surprising connection between Menger's classical covering property and Blass-Laflamme's modern combinatorial notion of groupwise density. This connection implies a short proof of the groupwise density bound on the additivity number for Menger's property.
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  3.  1 DLs
    Boaz Tsaban & Lyubomyr Zdomskyy (2008). Combinatorial Images of Sets of Reals and Semifilter Trichotomy. Journal of Symbolic Logic 73 (4):1278-1288.
    Using a dictionary translating a variety of classical and modern covering properties into combinatorial properties of continuous images, we get a simple way to understand the interrelations between these properties in ZFC and in the realm of the trichotomy axiom for upward closed families of sets of natural numbers. While it is now known that the answer to the Hurewicz 1927 problem is positive, it is shown here that semifilter trichotomy implies a negative answer to a slightly stronger form of (...)
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  4.  0 DLs
    Heike Mildenberger, Saharon Shelah & Boaz Tsaban (2006). Covering the Baire Space by Families Which Are Not Finitely Dominating. Annals of Pure and Applied Logic 140 (1):60-71.
    It is consistent that each union of many families in the Baire space which are not finitely dominating is not dominating. In particular, it is consistent that for each nonprincipal ultrafilter , the cofinality of the reduced ultrapower is greater than . The model is constructed by oracle chain condition forcing, to which we give a self-contained introduction.
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    Boaz Tsaban (2004). The Combinatorics of Splittability. 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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  6.  0 DLs
    Arnold W. Miller, Boaz Tsaban & Lyubomyr Zdomskyy (2014). Selective Covering Properties of Product Spaces. 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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