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Not every  -set is perfectly meager in the transitive sense
Author(s):
Andrzej
Nowik;
Tomasz
Weiss
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3017-3024.
MSC (2000):
Primary 03E15, 03E20, 28E15
Posted:
May 12, 2000
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Abstract:
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.
References:
-
- [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.
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Additional Information:
Andrzej
Nowik
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 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:
10.1090/S0002-9939-00-05355-7
PII:
S 0002-9939(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
Posted:
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 of article:
Copyright
2000,
American Mathematical Society
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