Not every -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

Published electronically:
May 12, 2000

MathSciNet review:
1664434

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

We prove the following theorems:

- 1.
- It is consistent with ZFC that there exists a - set which is not perfectly meager in the transitive sense.
- 2.
- Every set which is perfectly meager in the transitive sense has the 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:
http://dx.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