12 found
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  1.  15
    Mathias Forcing and Combinatorial Covering Properties of Filters.David Chodounský, Dušan Repovš & Lyubomyr Zdomskyy - 2015 - Journal of Symbolic Logic 80 (4):1398-1410.
    We give topological characterizations of filters${\cal F}$onωsuch that the Mathias forcing${M_{\cal F}}$adds no dominating reals or preserves ground model unbounded families. This allows us to answer some questions of Brendle, Guzmán, Hrušák, Martínez, Minami, and Tsaban.
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  2.  41
    Projective Wellorders and Mad Families with Large Continuum.Vera Fischer, Sy David Friedman & Lyubomyr Zdomskyy - 2011 - Annals of Pure and Applied Logic 162 (11):853-862.
    We show that is consistent with the existence of a -definable wellorder of the reals and a -definable ω-mad subfamily of [ω]ω.
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  3.  30
    Fusion and Large Cardinal Preservation.Sy-David Friedman, Radek Honzik & Lyubomyr Zdomskyy - 2013 - Annals of Pure and Applied Logic 164 (12):1247-1273.
    In this paper we introduce some fusion properties of forcing notions which guarantee that an iteration with supports of size ⩽κ not only does not collapse κ+ but also preserves the strength of κ. This provides a general theory covering the known cases of tree iterations which preserve large cardinals [3], Friedman and Halilović [5], Friedman and Honzik [6], Friedman and Magidor [8], Friedman and Zdomskyy [10], Honzik [12]).
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  4.  44
    Projective Mad Families.Sy-David Friedman & Lyubomyr Zdomskyy - 2010 - Annals of Pure and Applied Logic 161 (12):1581-1587.
    Using almost disjoint coding we prove the consistency of the existence of a definable ω-mad family of infinite subsets of ω together with.
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  5.  9
    Products of Hurewicz Spaces in the Laver Model.Dušan Repovš & Lyubomyr Zdomskyy - 2017 - Bulletin of Symbolic Logic 23 (3):324-333.
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  6.  7
    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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  7.  33
    Cardinal Characteristics, Projective Wellorders and Large Continuum.Vera Fischer, Sy David Friedman & Lyubomyr Zdomskyy - 2013 - Annals of Pure and Applied Logic 164 (7-8):763-770.
    We extend the work of Fischer et al. [6] by presenting a method for controlling cardinal characteristics in the presence of a projective wellorder and 2ℵ0>ℵ2. This also answers a question of Harrington [9] by showing that the existence of a Δ31 wellorder of the reals is consistent with Martinʼs axiom and 2ℵ0=ℵ3.
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  8.  8
    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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  9.  2
    Covering Properties of $$Omega $$-Mad Families.Leandro Aurichi & Lyubomyr Zdomskyy - forthcoming - Archive for Mathematical Logic:1-8.
    We prove that Martin’s Axiom implies the existence of a Cohen-indestructible mad family such that the Mathias forcing associated to its filter adds dominating reals, while \ is consistent with the negation of this statement as witnessed by the Laver model for the consistency of Borel’s conjecture.
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  10.  25
    On the Length of Chains of Proper Subgroups Covering a Topological Group.Taras Banakh, Dušan Repovš & Lyubomyr Zdomskyy - 2011 - Archive for Mathematical Logic 50 (3-4):411-421.
    We prove that if an ultrafilter ${\mathcal{L}}$ is not coherent to a Q-point, then each analytic non-σ-bounded topological group G admits an increasing chain ${\langle G_\alpha:\alpha < \mathfrak b(\mathcal L)\rangle}$ of its proper subgroups such that: (i) ${\bigcup_{\alpha}G_\alpha=G}$ ; and (ii) For every σ-bounded subgroup H of G there exists α such that ${H\subset G_\alpha}$ . In case of the group Sym(ω) of all permutations of ω with the topology inherited from ω ω this improves upon earlier results of S. (...)
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  11.  18
    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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  12.  3
    Between Polish and Completely Baire.Andrea Medini & Lyubomyr Zdomskyy - 2015 - Archive for Mathematical Logic 54 (1-2):231-245.
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