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  1.  12
    Covering Properties of Ideals.Marek Balcerzak, Barnabás Farkas & Szymon Gła̧b - 2013 - Archive for Mathematical Logic 52 (3-4):279-294.
    Elekes proved that any infinite-fold cover of a σ-finite measure space by a sequence of measurable sets has a subsequence with the same property such that the set of indices of this subsequence has density zero. Applying this theorem he gave a new proof for the random-indestructibility of the density zero ideal. He asked about other variants of this theorem concerning I-almost everywhere infinite-fold covers of Polish spaces where I is a σ-ideal on the space and the set of indices (...)
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  2.  43
    Hechler's Theorem for Tall Analytic P-Ideals.Barnabás Farkas - 2011 - Journal of Symbolic Logic 76 (2):729 - 736.
    We prove the following version of Hechler's classical theorem: For each partially ordered set (Q, ≤) with the property that every countable subset of Q has a strict upper bound in Q, there is a ccc forcing notion such that in the generic extension for each tall analytic P-ideal J (coded in the ground model) a cofinal subset of (J, ⊆*) is order isomorphic to (Q, ≤).
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  3.  12
    Towers in Filters, Cardinal Invariants, and Luzin Type Families.Jörg Brendle, Barnabás Farkas & Jonathan Verner - 2018 - Journal of Symbolic Logic 83 (3):1013-1062.
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  4.  37
    Cardinal Coefficients Associated to Certain Orders on Ideals.Piotr Borodulin-Nadzieja & Barnabás Farkas - 2012 - Archive for Mathematical Logic 51 (1-2):187-202.
    We study cardinal invariants connected to certain classical orderings on the family of ideals on ω. We give topological and analytic characterizations of these invariants using the idealized version of Fréchet-Urysohn property and, in a special case, using sequential properties of the space of finitely-supported probability measures with the weak* topology. We investigate consistency of some inequalities between these invariants and classical ones, and other related combinatorial questions. At last, we discuss maximality properties of almost disjoint families related to certain (...)
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  5.  5
    Representations of Ideals in Polish Groups and in Banach Spaces.Piotr Borodulin–Nadzieja, Barnabás Farkas & Grzegorz Plebanek - 2015 - Journal of Symbolic Logic 80 (4):1268-1289.
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