Ukrainian Mathematical Journal

, Volume 42, Issue 6, pp 751–754 | Cite as

A two-coloring of Cartesian products

  • E. G. Zelenyuk
  • V. I. Malykhin
Brief Communications


We shall color the Cartesian product ω × ω1with two colors. Can an infinite subset A ⊂ω and an uncountable subset B ⊂ω1 be found such that the product A × B can be one-colored? This problem proves to be unsolvable in ZFC.


Infinite Subset Uncountable Subset 
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Literature cited

  1. 1.
    P. Erdös and R. Rado, “Combinatorial theorems on classifications of subsets of a given set,” Proc. London Math. Soc.,2, No. 3, 417–439 (1952).Google Scholar
  2. 2.
    J. Barwise (ed.), Handbook of Mathematical Logic, Set Theory, North-Holland, Amsterdam (1977).Google Scholar
  3. 3.
    V. I. Malykhin, “Topological properties of Cohen's generic extensions,” Dokl. Akad. Nauk SSSR,274, No. 3, 540–544 (1984).Google Scholar
  4. 4.
    V. I. Malykhin, “Existence of topological objects for an arbitrary cardinal arithmetic,” Dokl. Akad. Nauk SSSR,286, No. 3, 542–546 (1986).Google Scholar
  5. 5.
    K. Kunen and I. E. Vaughan (eds.), Handbook of Set-Theoretic Topology, North-Holland, Amsterdam (1984).Google Scholar
  6. 6.
    K. Kunen, Set Theory, North-Holland, Amsterdam (1980).Google Scholar
  7. 7.
    V. I. Arnautov, A. V. Arkhangel'skii, P. I. Kirku, et al. (eds.), Unsolved Problems in Topological Algebra, Shtiintsa, Kishinev (1985).Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • E. G. Zelenyuk
    • 1
  • V. I. Malykhin
    • 1
  1. 1.Kiev UniversityUSSR

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