The least cardinal for which the Baire category theorem fails

The least cardinal for which the Baire category theorem fails
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by Marion Scheepers PDF

Proc. Amer. Math. Soc. 125 (1997), 579-585 Request permission

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

References

Tomek Bartoszyński, Combinatorial aspects of measure and category, Fund. Math. 127 (1987), no. 3, 225–239. MR 917147, DOI 10.4064/fm-127-3-225-239
R. Michael Canjar, On the generic existence of special ultrafilters, Proc. Amer. Math. Soc. 110 (1990), no. 1, 233–241. MR 993747, DOI 10.1090/S0002-9939-1990-0993747-3
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
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 493925
W. Just, A. W. Miller, M. Scheepers, and P. Szeptycki, Combinatorics of open covers (II), Topology and Its Applications (to appear).
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, DOI 10.1090/S0002-9939-1982-0671224-2
F. Rothberger, Eine Verschärfung der Eigenschaft $C$, Fundamenta Mathematicae 30 (1938), 50–55.
M. Scheepers, Meager sets and infinite games, Contemporary Mathematics 192 (1996), 77–90.
M. Scheepers, Combinatorics of open covers (I): Ramsey theory, Topology and Its Applications 69 (1996), 31–62.