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
DOI:
https://doi.org/10.1090/S0002-9939-00-05355-7
Published electronically:
May 12, 2000
MathSciNet review:
1664434
Full-text PDF
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.
- [G1] E.Grzegorek `Always of the first category sets' Proceedings of the 12th Winter School on Abstract Amalysis Srni(Bohemian Weald), 15-29 January, 1984, Section of Topology, Supplemento ai Rend. Circ. Mat. Palermo, Serie II-numero 6-1984, 139-147 MR 86a:00004
- [G2] E.Grzegorek `Always of the first category sets (II)' Proceedings of the 13th Winter School on Abstract Amalysis Srni(Bohemian Weald), 20-27 January, 1985, Section of Topology, Supplemento ai Rend. Circ. Mat. Palermo, Serie II-numero 10-1985, 43-48 MR 88j:54054
- [JS] H. Judah, S. Shelah, Q-sets, Sierpinski sets, Rapid filters. Proceedings of the American Mathematical Society, 111. 1991, 821 - 832. MR 91f:03105
- [M] A.W. Miller `Special subsets of the real line' in `Handbook of set - theoretic topology', 1984b, 201 - 233, North - Holland, Amsterdam - New York. MR 86i:54037
- [NSW] A. Nowik, M. Scheepers, T. Weiss. The algebraic sum of sets of real numbers with strong measure zero sets, Journal of Symbolic Logic vol. 63(1), 1998, 301 - 324. MR 99c:54049
- [R]
I. Rec
aw, Some additive properties of special subsets of the real line, Colloquium Mathematicum, vol LXII, 1991. MR 93b:28003
- [vN] J.v. Neumann, Ein System algebraisch unabhängiger Zahlen, Math. Ann. 99, 1928.
- [Z] P. Zakrzewski, Universally meager sets, to appear.
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 03E15, 03E20, 28E15
Retrieve articles in all journals with MSC (2000): 03E15, 03E20, 28E15
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