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The least cardinal for which the Baire category theorem fails
Author(s):
Marion
Scheepers
Journal:
Proc. Amer. Math. Soc.
125
(1997),
579-585.
MSC (1991):
Primary 03E20, 04A20
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Abstract:
The least cardinal for which the Baire category theorem fails is equal to the least cardinal for which a Ramseyan theorem fails.
References:
- 1.
- Tomek Bartoszynski, Combinatorial aspects of measure and category, Fundamenta Mathematicae 127 (1987), 225-239. MR 88m:04001
- 2.
- R. M. Canjar, On the generic existence of special ultrafilters, Proceedings of the American Mathematical Society 110 (1990), 233-241. MR 90m:03083
- 3.
- P. Erdös, A. Hajnal, A. Mate, and R. Rado, Combinatorial Set Theory: Partition relations for cardinals, North-Holland (1984). MR 87g:04002
- 4.
- F. Galvin, Indeterminacy of point-open games, Bulletin of the Polish Academy of Sciences (Series Sciences, Mathematics and Astronomy 26 (1978), 445-448. MR 58:12881
- 5.
- W. Just, A. W. Miller, M. Scheepers, and P. Szeptycki, Combinatorics of open covers (II), Topology and Its Applications (to appear).
- 6.
- A. W. Miller, A characterization of the least cardinal for which the Baire Category Theorem fails, Proceedings of the American Mathematical Society 86 (1982), 498-502. MR 84b:04002
- 7.
- F. Rothberger, Eine Verschärfung der Eigenschaft
 , Fundamenta Mathematicae 30 (1938), 50-55. - 8.
- M. Scheepers, Meager sets and infinite games, Contemporary Mathematics 192 (1996), 77-90. CMP 96:06
- 9.
- M. Scheepers, Combinatorics of open covers (I): Ramsey theory, Topology and Its Applications 69 (1996), 31-62. CMP 96:09
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Additional Information:
Marion
Scheepers
Affiliation:
Department of Mathematics, Boise State University, Boise, Idaho 83725-0001
Email:
marion@cantor.idbsu.edu
DOI:
10.1090/S0002-9939-97-03597-1
PII:
S 0002-9939(97)03597-1
Received by editor(s):
December 14, 1994
Received by editor(s) in revised form:
July 17, 1995
Communicated by:
Andreas R. Blass
Copyright of article:
Copyright
1997,
American Mathematical Society
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