9 found
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  1.  13
    Semimorasses and Nonreflection at Singular Cardinals.Piotr Koszmider - 1995 - Annals of Pure and Applied Logic 72 (1):1-23.
    Some subfamilies of κ, for κ regular, κ λ, called -semimorasses are investigated. For λ = κ+, they constitute weak versions of Velleman's simplified -morasses, and for λ > κ+, they provide a combinatorial framework which in some cases has similar applications to the application of -morasses with this difference that the obtained objects are of size λ κ+, and not only of size κ+ as in the case of morasses. New consistency results involve existence of nonreflecting objects of singular (...)
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  2. On the Existence of Strong Chains in ℘(Ω1)/Fin.Piotr Koszmider - 1998 - Journal of Symbolic Logic 63 (3):1055 - 1062.
    $(X_\alpha: \alpha is a strong chain in ℘(ω 1 )/Fin if and only if X β - X α is finite and X α - X β is uncountable for each $\beta . We show that it is consistent that a strong chain in ℘(ω 1 ) exists. On the other hand we show that it is consistent that there is a strongly almost-disjoint family in ℘(ω 1 ) but no strong chain exists: □ ω 1 is used to construct (...)
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  3. On Coherent Families of Finite-to-One Functions.Piotr Koszmider - 1993 - Journal of Symbolic Logic 58 (1):128-138.
    We consider the existence of coherent families of finite-to-one functions on countable subsets of an uncountable cardinal κ. The existence of such families for κ implies the existence of a winning 2-tactic for player TWO in the countable-finite game on κ. We prove that coherent families exist on κ = ωn, where n ∈ ω, and that they consistently exist for every cardinal κ. We also prove that iterations of Axiom A forcings with countable supports are Axiom A.
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  4.  6
    On Constructions with 2-Cardinals.Piotr Koszmider - 2017 - Archive for Mathematical Logic 56 (7-8):849-876.
    We propose developing the theory of consequences of morasses relevant in mathematical applications in the language alternative to the usual one, replacing commonly used structures by families of sets originating with Velleman’s neat simplified morasses called 2-cardinals. The theory of related trees, gaps, colorings of pairs and forcing notions is reformulated and sketched from a unifying point of view with the focus on the applicability to constructions of mathematical structures like Boolean algebras, Banach spaces or compact spaces. The paper is (...)
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  5. REVIEWS-Papers-Set-Theoretic Methods in Topology.Z. Szentmiklossy, Z. Balogh & Piotr Koszmider - 2002 - Bulletin of Symbolic Logic 8 (2):306-306.
  6.  28
    S-Spaces and L-Spaces Under Martin's AxiomOn Compact Hausdorff Spaces of Countable Tightness.Piotr Koszmider, Z. Szentmiklossy, A. Csaszar & Zoltan Balogh - 2002 - Bulletin of Symbolic Logic 8 (2):306.
  7.  25
    A Formalism for Some Class of Forcing Notions.Piotr Koszmider & P. Koszmider - 1992 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 38 (1):413-421.
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  8.  22
    Szentmiklóssy Z.. S-Spaces and L-Spaces Under Martin's Axiom. Topology, Volume II, Edited by Császár A., Colloquia Mathematica Societatis János Bolyai, No. 23, János Bolyai Mathematical Society, Budapest, and North-Holland Publishing Company, Amsterdam, Oxford, and New York, 1980, Pp. 1139–1145. Balogh Zoltán. On Compact Hausdorff Spaces of Countable Tightness. Proceedings of the American Mathematical Society, Vol. 105 (1989), Pp. 755–764. [REVIEW]Piotr Koszmider - 2002 - Bulletin of Symbolic Logic 8 (2):306-307.
  9.  8
    A Formalism for Some Class of Forcing Notions.Piotr Koszmider & P. Koszmider - 1992 - Mathematical Logic Quarterly 38 (1):413-421.
    We introduce a class of forcing notions, called forcing notions of type S, which contains among other Sacks forcing, Prikry-Silver forcing and their iterations and products with countable supports. We construct and investigate some formalism suitable for this forcing notions, which allows all standard tricks for iterations or products with countable supports of Sacks forcing. On the other hand it does not involve internal combinatorial structure of conditions of iterations or products. We prove that the class of forcing notions of (...)
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