The least cardinal for which

the Baire category theorem fails

Author:
Marion Scheepers

Journal:
Proc. Amer. Math. Soc. **125** (1997), 579-585

MSC (1991):
Primary 03E20, 04A20

DOI:
https://doi.org/10.1090/S0002-9939-97-03597-1

MathSciNet review:
1350961

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Abstract | References | Similar Articles | Additional Information

Abstract: The least cardinal for which the Baire category theorem fails is equal to the least cardinal for which a Ramseyan theorem fails.

**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:
https://doi.org/10.1090/S0002-9939-97-03597-1

Received by editor(s):
December 14, 1994

Received by editor(s) in revised form:
July 17, 1995

Communicated by:
Andreas R. Blass

Article copyright:
© Copyright 1997
American Mathematical Society