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

MathSciNet review:
1350961

Full-text PDF Free Access

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 Bartoszyński,*Combinatorial aspects of measure and category*, Fund. Math.**127**(1987), no. 3, 225–239. MR**917147****2.**R. Michael Canjar,*On the generic existence of special ultrafilters*, Proc. Amer. Math. Soc.**110**(1990), no. 1, 233–241. MR**993747**, 10.1090/S0002-9939-1990-0993747-3**3.**Paul Erdős, András Hajnal, Attila Máté, and Richard Rado,*Combinatorial set theory: partition relations for cardinals*, Studies in Logic and the Foundations of Mathematics, vol. 106, North-Holland Publishing Co., Amsterdam, 1984. MR**795592****4.**Fred Galvin,*Indeterminacy of point-open games*, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.**26**(1978), no. 5, 445–449 (English, with Russian summary). MR**0493925****5.**W. Just, A. W. Miller, M. Scheepers, and P. Szeptycki,*Combinatorics of open covers*(II), Topology and Its Applications (to appear).**6.**Arnold W. Miller,*A characterization of the least cardinal for which the Baire category theorem fails*, Proc. Amer. Math. Soc.**86**(1982), no. 3, 498–502. MR**671224**, 10.1090/S0002-9939-1982-0671224-2**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**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
03E20,
04A20

Retrieve articles in all journals with MSC (1991): 03E20, 04A20

Additional Information

**Marion Scheepers**

Affiliation:
Department of Mathematics, Boise State University, Boise, Idaho 83725-0001

Email:
marion@cantor.idbsu.edu

DOI:
http://dx.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