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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Not every $Q$-set is perfectly meager in the transitive sense
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by Andrzej Nowik and Tomasz Weiss
Proc. Amer. Math. Soc. 128 (2000), 3017-3024
DOI: https://doi.org/10.1090/S0002-9939-00-05355-7
Published electronically: May 12, 2000

Abstract:

We prove the following theorems:

  1. It is consistent with ZFC that there exists a $Q$ - set which is not perfectly meager in the transitive sense.

  2. Every set which is perfectly meager in the transitive sense has the ${\overline {AFC}}$ property.

  3. The product of two sets perfectly meager in the transitive sense has also that property.

References
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Bibliographic Information
  • Andrzej Nowik
  • Affiliation: Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00 – 950 Warsaw, Poland
  • Email: matan@paula.univ.gda.pl
  • Tomasz Weiss
  • Affiliation: Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
  • Address at time of publication: Institute of Mathematics, WSRP, 08-110 Siedlce, Poland
  • MR Author ID: 631175
  • ORCID: 0000-0001-9201-7202
  • Email: weiss@wsrp.siedlce.pl
  • Received by editor(s): October 6, 1997
  • Received by editor(s) in revised form: September 16, 1998, and November 9, 1998
  • Published electronically: May 12, 2000
  • Additional Notes: The first author was partially supported by the KBN grant 2 P03A 047 09.
  • Communicated by: Carl G. Jockusch, Jr.
  • © Copyright 2000 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 128 (2000), 3017-3024
  • MSC (2000): Primary 03E15, 03E20, 28E15
  • DOI: https://doi.org/10.1090/S0002-9939-00-05355-7
  • MathSciNet review: 1664434