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Not every $Q$-set is perfectly meager in the transitive sense


Authors: Andrzej Nowik and Tomasz Weiss
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
Published electronically: May 12, 2000
MathSciNet review: 1664434
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Abstract | References | Similar Articles | Additional Information

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.


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Additional 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
Email: weiss@wsrp.siedlce.pl

DOI: https://doi.org/10.1090/S0002-9939-00-05355-7
Keywords: Strongly first category set, always first category set, $Q$ -- set
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.
Article copyright: © Copyright 2000 American Mathematical Society

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