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Jacek Cichoń [4]J. Cichoń [4]
  1. Dualization of the Van Douwen Diagram.Jacek Cichoń, Adam Krawczyk, Barbara Majcher-Iwanow & Bogdan Wȩglorz - 2000 - Journal of Symbolic Logic 65 (2):959-968.
    We make a more systematic study of the van Douwen diagram for cardinal coefficients related to combinatorial properties of partitions of natural numbers.
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  2. Combinatorial Properties of the Ideal ℬ2.J. Cichon, A. Roslanowski, J. Steprans & B. Weglorz - 1993 - Journal of Symbolic Logic 58 (1):42-54.
    By B2 we denote the σ-ideal of all subsets A of the Cantor set {0,1}ω such that for every infinite subset T of ω the restriction A∣{0,1}T is a proper subset of {0,1}T. In this paper we investigate set theoretical properties of this and similar ideals.
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  3. 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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    Decomposing Baire Functions.J. Cichoń, M. Morayne, J. Pawlikowski & S. Solecki - 1991 - Journal of Symbolic Logic 56 (4):1273 - 1283.
    We discuss in the paper the following problem: Given a function in a given Baire class, into "how many" (in terms of cardinal numbers) functions of lower classes can it be decomposed? The decomposition is understood here in the sense of the set-theoretical union.
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    Combinatorial Properties of the Ideal $Mathfrak{B}_2$.J. Cichon, A. Roslanowski, J. Steprans & B. Weglorz - 1993 - Journal of Symbolic Logic 58 (1):42-54.
    By $\mathfrak{B}_2$ we denote the $\sigma$-ideal of all subsets $A$ of the Cantor set $\{0,1\}^\omega$ such that for every infinite subset $T$ of $\omega$ the restriction $A\mid\{0,1\}^T$ is a proper subset of $\{0,1\}^T$. In this paper we investigate set theoretical properties of this and similar ideals.
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    On the Compactness of Some Boolean Algebras.Jacek Cichoń - 1984 - Journal of Symbolic Logic 49 (1):63-67.
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    Hamel-Isomorphic Images of the Unit Ball.Jacek Cichoń & Przemysław Szczepaniak - 2010 - Mathematical Logic Quarterly 56 (6):625-630.
    In this article we consider linear isomorphisms over the field of rational numbers between the linear spaces ℝ2 and ℝ. We prove that if f is such an isomorphism, then the image by f of the unit disk is a strictly nonmeasurable subset of the real line, which has different properties than classical non-measurable subsets of reals. We shall also consider the question whether all images of bounded measurable subsets of the plane via a such mapping are non-measurable.
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