1.  28
    Decomposing Borel Functions and Structure at Finite Levels of the Baire Hierarchy.Janusz Pawlikowski & Marcin Sabok - 2012 - Annals of Pure and Applied Logic 163 (12):1748-1764.
    We prove that if f is a partial Borel function from one Polish space to another, then either f can be decomposed into countably many partial continuous functions, or else f contains the countable infinite power of a bijection that maps a convergent sequence together with its limit onto a discrete space. This is a generalization of a dichotomy discovered by Solecki for Baire class 1 functions. As an application, we provide a characterization of functions which are countable unions of (...)
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  2.  19
    Forcing Properties of Ideals of Closed Sets.Marcin Sabok & Jindřich Zapletal - 2011 - Journal of Symbolic Logic 76 (3):1075 - 1095.
    With every σ-ideal I on a Polish space we associate the σ-ideal I* generated by the closed sets in I. We study the forcing notions of Borel sets modulo the respective σ-ideals I and I* and find connections between their forcing properties. To this end, we associate to a σ-ideal on a Polish space an ideal on a countable set and show how forcing properties of the forcing depend on combinatorial properties of the ideal. We also study the 1—1 or (...)
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  3.  24
    Σ-Continuity and Related Forcings.Marcin Sabok - 2009 - Archive for Mathematical Logic 48 (5):449-464.
    The Steprāns forcing notion arises as quotient of the algebra of Borel sets modulo the ideal of σ-continuity of a certain Borel not σ-continuous function. We give a characterization of this forcing in the language of trees and use this characterization to establish such properties of the forcing as fusion and continuous reading of names. Although the latter property is usually implied by the fact that the associated ideal is generated by closed sets, we show that it is not the (...)
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  4.  9
    Baumgartnerʼs Conjecture and Bounded Forcing Axioms.David Asperó, Sy-David Friedman, Miguel Angel Mota & Marcin Sabok - 2013 - Annals of Pure and Applied Logic 164 (12):1178-1186.
  5.  32
    Two Stars.Janusz Pawlikowski & Marcin Sabok - 2008 - Archive for Mathematical Logic 47 (7-8):673-676.
    The authors investigate an operation * on the subsets of ${\mathcal{P}(\mathbb{R})}$ . It is connected with Borel’s strong measure zero sets as well as strongly meager. The results concern the behaviour of the family of countable sets when * is applied.
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