14 found
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  1. On Ideals of Subsets of the Plane and on Cohen Reals.Jacek Cichoń & Janusz Pawlikowski - 1986 - Journal of Symbolic Logic 51 (3):560-569.
    Let J be any proper ideal of subsets of the real line R which contains all finite subsets of R. We define an ideal J * ∣B as follows: X ∈ J * ∣B if there exists a Borel set $B \subset R \times R$ such that $X \subset B$ and for any x ∈ R we have $\{y \in R: \langle x,y\rangle \in B\} \in \mathscr{J}$ . We show that there exists a family $\mathscr{A} \subset \mathscr{J}^\ast\mid\mathscr{B}$ of power ω (...)
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  2.  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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  3.  12
    Why Solovay Real Produces Cohen Real.Janusz Pawlikowski - 1986 - Journal of Symbolic Logic 51 (4):957-968.
    An explanation is given of why, after adding to a model M of ZFC first a Solovay real r and next a Cohen real c, in M[ r][ c] a Cohen real over M[ c] is produced. It is also shown that a Solovay algebra iterated with a Cohen algebra can be embedded into a Cohen algebra iterated with a Solovay algebra.
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  4.  12
    Every Sierpiński Set is Strongly Meager.Janusz Pawlikowski - 1996 - Archive for Mathematical Logic 35 (5-6):281-285.
  5.  12
    Adding Dominating Reals with Ωω Bounding Posets.Janusz Pawlikowski - 1992 - Journal of Symbolic Logic 57 (2):540 - 547.
  6.  8
    Adding Dominating Reals With $Omega^Omega$ Bounding Posets.Janusz Pawlikowski - 1992 - Journal of Symbolic Logic 57 (2):540-547.
  7.  14
    Extending Baire Property by Uncountably Many Sets.Paweł Kawa & Janusz Pawlikowski - 2010 - Journal of Symbolic Logic 75 (3):896-904.
    We show that for an uncountable κ in a suitable Cohen real model for any family {A ν } ν<κ of sets of reals there is a σ-homomorphism h from the σ-algebra generated by Borel sets and the sets A ν into the algebra of Baire subsets of 2 κ modulo meager sets such that for all Borel B, B is meager iff h(B) = 0. The proof is uniform, works also for random reals and the Lebesgue measure, and in (...)
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  8. 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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  9. Cohen Reals From Small Forcings.Janusz Pawlikowski - 2001 - Journal of Symbolic Logic 66 (1):318-324.
    We introduce a new cardinal characteristic r*, related to the reaping number r, and show that posets of size $ r* which add reals add unbounded reals; posets of size $ r which add unbounded reals add Cohen reals. We also show that add(M) ≤ min(r, r*). It follows that posets of size < add(M) which add reals add Cohen reals. This improves results of Roslanowski and Shelah [RS] and of Zapletal [Z].
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  10.  3
    Density Zero Slaloms.Janusz Pawlikowski - 2000 - Annals of Pure and Applied Logic 103 (1-3):39-53.
    We construct a G δ set G ⊆ ω ω ×2 ω with null vertical sections such that each perfect set P ⊆2 ω meets almost all vertical sections of G in the following sense: we can define from P subsets S of ω of density zero such that whenever the section determined by x ∈ ω ω does not meet P , then x ∈ S for all but finitely many i . This generalizes theorems of Mokobodzki and Brendle (...)
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  11.  50
    Finite Support Iteration and Strong Measure Zero Sets.Janusz Pawlikowski - 1990 - Journal of Symbolic Logic 55 (2):674-677.
    Any finite support iteration of posets with precalibre ℵ 1 which has the length of cofinality greater than ω 1 yields a model for the dual Borel conjecture in which the real line is covered by ℵ 1 strong measure zero sets.
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  12.  4
    Mathias Forcing and Ultrafilters.Janusz Pawlikowski & Wojciech Stadnicki - 2016 - Archive for Mathematical Logic 55 (7-8):857-865.
    We prove that if the Mathias forcing is followed by a forcing with the Laver Property, then any V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {V}$$\end{document}-q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {q}$$\end{document}-point is isomorphic via a ground model bijection to the canonical V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {V}$$\end{document}-Ramsey ultrafilter added by the Mathias real. This improves a result of Shelah and Spinas.
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  13. The Diamond Covering Property Axiom.Janusz Pawlikowski - 2016 - Mathematical Logic Quarterly 62 (4-5):407-411.
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  14.  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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