Perfectly meager sets and universally null sets
Authors:
Tomek Bartoszynski and Saharon Shelah
Journal:
Proc. Amer. Math. Soc. 130 (2002), 3701-3711
MSC (2000):
Primary 03E17
DOI:
https://doi.org/10.1090/S0002-9939-02-06465-1
Published electronically:
April 22, 2002
MathSciNet review:
1920051
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We will show that there is no $\operatorname {\mathsf {ZFC}}$ example of a set distinguishing between universally null and perfectly meager sets.
- Tomek Bartoszyński. Measure and Category Invariants. In M. Magidor, M. Foreman, A. Kanamori, editors, Handbook of Set Theory. submitted.
- Tomek Bartoszynski. On perfectly meager sets. Proceedings of the American Mathematical Society, 130(4):1189–1195, 2002.
- Tomek Bartoszyński and Haim Judah, Set theory, A K Peters, Ltd., Wellesley, MA, 1995. On the structure of the real line. MR 1350295
- Paul Corazza, The generalized Borel conjecture and strongly proper orders, Trans. Amer. Math. Soc. 316 (1989), no. 1, 115–140. MR 982239, DOI https://doi.org/10.1090/S0002-9947-1989-0982239-X
- Martin Goldstern, Haim Judah, and Saharon Shelah, Strong measure zero sets without Cohen reals, J. Symbolic Logic 58 (1993), no. 4, 1323–1341. MR 1253925, DOI https://doi.org/10.2307/2275146
- Edward Grzegorek, Solution of a problem of Banach on $\sigma $-fields without continuous measures, Bull. Acad. Polon. Sci. Sér. Sci. Math. 28 (1980), no. 1-2, 7–10 (1981) (English, with Russian summary). MR 616191
- Arnold W. Miller, Some properties of measure and category, Trans. Amer. Math. Soc. 266 (1981), no. 1, 93–114. MR 613787, DOI https://doi.org/10.1090/S0002-9947-1981-0613787-2
- Arnold W. Miller, Mapping a set of reals onto the reals, J. Symbolic Logic 48 (1983), no. 3, 575–584. MR 716618, DOI https://doi.org/10.2307/2273449
- Arnold W. Miller, Special subsets of the real line, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 201–233. MR 776624
- Andrzej Rosłanowski and Saharon Shelah, Norms on possibilities. I. Forcing with trees and creatures, Mem. Amer. Math. Soc. 141 (1999), no. 671, xii+167. MR 1613600, DOI https://doi.org/10.1090/memo/0671
- Saharon Shelah. Proper and Improper Forcing. Perspectives in Logic. Springer-Verlag, 1998.
- Waclaw Sierpiński. Sur une probleme de M. Kuratowski concernant la propriete de Baire des ensambles. Fundamenta Mathematicae, 22:262–266, 1934.
- Piotr Zakrzewski, Universally meager sets, Proc. Amer. Math. Soc. 129 (2001), no. 6, 1793–1798. MR 1814112, DOI https://doi.org/10.1090/S0002-9939-00-05726-9
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 03E17
Retrieve articles in all journals with MSC (2000): 03E17
Additional Information
Tomek Bartoszynski
Affiliation:
Department of Mathematics and Computer Science, Boise State University, Boise, Idaho 83725
Email:
tomek@math.boisestate.edu
Saharon Shelah
Affiliation:
Department of Mathematics, Hebrew University, Jerusalem, Israel – and – Department of Mathematics, Rutgers University, New Brunswick, New Jersey
MR Author ID:
160185
ORCID:
0000-0003-0462-3152
Email:
shelah@math.huji.ac.il
Keywords:
Perfectly meager,
universally null,
consistency
Received by editor(s):
April 26, 2001
Received by editor(s) in revised form:
July 16, 2001
Published electronically:
April 22, 2002
Additional Notes:
The first author was partially supported by NSF grant DMS 9971282 and the Alexander von Humboldt Foundation
The second author was partially supported by the Israel Science Foundation. Publication 732
Communicated by:
Alan Dow
Article copyright:
© Copyright 2002
American Mathematical Society
