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
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Abstract:
We prove the following theorems:
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It is consistent with ZFC that there exists a $Q$ - set which is not perfectly meager in the transitive sense.
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Every set which is perfectly meager in the transitive sense has the ${\overline {AFC}}$ property.
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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