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On perfectly meager sets


Author: Tomek Bartoszynski
Journal: Proc. Amer. Math. Soc. 130 (2002), 1189-1195
MSC (1991): Primary 03E17
DOI: https://doi.org/10.1090/S0002-9939-01-06138-X
Published electronically: October 1, 2001
MathSciNet review: 1873796
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Abstract: We show that it is consistent that the product of perfectly meager sets is perfectly meager.


References [Enhancements On Off] (What's this?)

  • 1. Tomek Bartoszynski and Haim Judah.
    Set Theory: on the structure of the real line.
    A.K. Peters, 1995. MR 96k:03002
  • 2. Haim Judah and Saharon Shelah.
    Killing Luzin and Sierpinski sets.
    Proceedings of the American Mathematical Society, 120:917-920, 1994. MR 94e:03046
  • 3. Alexander Kechris.
    Classical Descriptive Set Theory, volume 156 of Graduate Texts in Mathematics.
    Springer Verlag, 1995.MR 96e:03057
  • 4. Edward Marczewski (Szpilrajn).
    Probleme 68.
    Fundamenta Mathematicae, 25:579, 1935.
  • 5. Arnold W. Miller.
    Special subsets of the real line.
    In K. Kunen and J. E. Vaughan, editors, Handbook of Set Theoretic Topology, pages 201-235. North-Holland, Amsterdam, 1984. MR 86i:54037
  • 6. Janusz Pawlikowski.
    Products of perfectly meager sets and Lusin's function.
    Proceedings of the American Mathematical Society, 107(3):811-815, 1989. MR 90b:54025
  • 7. Ireneusz Rec\law.
    Products of perfectly meagre sets.
    Proceedings of the American Mathematical Society, 112(4):1029-1031, 1991. MR 91j:28001
  • 8. Waclaw Sierpinski.
    Sur une probleme de M.Kuratowski concernant la propriete de Baire des ensambles.
    Fundamenta Mathematicae, 22:262-266, 1934.
  • 9. S.M Srivastava.
    A Course on Borel sets.
    Graduate Texts in Mathematics. Springer-Verlag, 1998. MR 99d:04002
  • 10. Piotr Zakrzewski.
    Universally meager sets.
    to appear in Proceedings of the American Mathematical Society.

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Additional Information

Tomek Bartoszynski
Affiliation: Department of Mathematics and Computer Science, Boise State University, Boise, Idaho 83725
Email: tomek@math.boisestate.edu

DOI: https://doi.org/10.1090/S0002-9939-01-06138-X
Keywords: Perfectly meager, products, consistency
Received by editor(s): May 5, 2000
Received by editor(s) in revised form: October 24, 2000
Published electronically: October 1, 2001
Additional Notes: The author was partially supported by NSF grant DMS 99271
Communicated by: Alan Dow
Article copyright: © Copyright 2001 American Mathematical Society

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