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  1. Combinatorial images of sets of reals and semifilter trichotomy.Boaz Tsaban & Lyubomyr Zdomskyy - 2008 - 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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  • Groupwise dense families.Heike Mildenberger - 2001 - Archive for Mathematical Logic 40 (2):93-112.
    We show that the Filter Dichotomy Principle implies that there are exactly four classes of ideals in the set of increasing functions from the natural numbers. We thus answer two open questions on consequences of ? < ?. We show that ? < ? implies that ? = ?, and that Filter Dichotomy together with ? < ? implies ? < ?. The technical means is the investigation of groupwise dense sets, ideals, filters and ultrafilters. With related techniques we prove (...)
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  • Q-pointness, p-pointness and feebleness of ideals.Pierre Matet & Janusz Pawlikowski - 2003 - Journal of Symbolic Logic 68 (1):235-261.
    We study the degree of (weak) Q-pointness, and that of (weak) P-pointness, of ideals on a regular infinite cardinal.
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  • Combinatorics and forcing with distributive ideals.Pierre Matet - 1997 - Annals of Pure and Applied Logic 86 (2):137-201.
    We present a version for κ-distributive ideals over a regular infinite cardinal κ of some of the combinatorial results of Mathias on happy families. We also study an associated notion of forcing, which is a generalization of Mathias forcing and of Prikry forcing.
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  • Combinatorics for the dominating and unsplitting numbers.Jason Aubrey - 2004 - Journal of Symbolic Logic 69 (2):482-498.
    In this paper we introduce a new property of families of functions on the Baire space, called pseudo-dominating, and apply the properties of these families to the study of cardinal characteristics of the continuum. We show that the minimum cardinality of a pseudo-dominating family is min{.
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  • Near coherence and filter games.Todd Eisworth - 2001 - Archive for Mathematical Logic 40 (3):235-242.
    We investigate a two-player game involving pairs of filters on ω. Our results generalize a result of Shelah ([7] Chapter VI) dealing with applications of game theory in the study of ultrafilters.
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  • Forcing and stable ordered–union ultrafilters.Todd Eisworth - 2002 - Journal of Symbolic Logic 67 (1):449-464.
    We investigate the effect of a variant of Matet forcing on ultrafilters in the ground model and give a characterization of those P-points that survive such forcing, answering a question left open by Blass [4]. We investigate the question of when this variant of Matet forcing can be used to diagonalize small filters without destroying P-points in the ground model. We also deal with the question of generic existence of stable ordered-union ultrafilters.
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  • Menger's Covering Property and Groupwise Density.Boaz Tsaban & Lyubomyr Zdomskyy - 2006 - 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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