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ISSN 1088-6826(e) ISSN 0002-9939(p)

A ZFC Dowker space in $\aleph _{\omega+1}$ : An application of pcf theory to topology

Author(s): Menachem Kojman; Saharon Shelah
Journal: Proc. Amer. Math. Soc. 126 (1998), 2459-2465.
MSC (1991): Primary 54B99, 54G99; Secondary 04A20, 04A30
MathSciNet review: 1605988
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Abstract: The existence of a Dowker space of cardinality $\aleph _{\omega+1}$ and weight $\aleph _{\omega+1}$ is proved in ZFC using pcf theory.

References:

1.: Zoltan T. Balogh, A small Dowker space in ZFC, Proc. Amer. Math. Soc. 124 (1996), no. 8, 2555-2560. MR 96j:54026
2.: Zoltan T. Balogh, A normal screenable nonparacompact space in ZFC, Proc. Amer. Math. Soc. 126 (1998), 1835-1844. CMP 97:15
3.: M. .R. Burke and M. Magidor, Shelah's pcf theory and its applications, Ann. Pure Appl. Logic 50 (1990) 207-254. MR 92f:03053
4.: C. H. Dowker, On countably paracompact spaces, Canad. J. Math. 3 (1951), 219-224. MR 13:264c
5.: M. Kojman, The A,B,C of pcf: a pcf companion, preprint.
6.: M. E. Rudin, A normal space $X$ for which $X\times I$ is not normal, Fund. Math. 73 (1971) 189-186. MR 45:2660
7.: M. E. Rudin, Dowker Spaces, in Handbook of set-theoretic topology, K. Kunen and J. E. Vaughan eds. Elsevier Science Publishers, 1984. MR 86c:54018
8.: S. Shelah, Cardinal Arithmetic, Oxford University Press, 1994. MR 96e:03001

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Additional Information:

Menachem Kojman
Affiliation: Department of Mathematics, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213
Address at time of publication: Department of Mathematics, Ben Gurion University of the Negev, POB 653, 84105 Beer-Sheva, Israel
Email: kojman@math.bgu.ac.il

Saharon Shelah
Affiliation: Institute of Mathematics, The Hebrew University of Jerusalem, and Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Email: shelah@math.huji.ac.il

DOI: 10.1090/S0002-9939-98-04884-9
PII: S 0002-9939(98)04884-9
Keywords: ZFC, Dowker space, cardinality, pcf theory
Received by editor(s): June 15, 1996
Additional Notes: The second author's research was supported by ``The Israel Science Foundation'' administered by The Israel Academy of Sciences and Humanities. Publication 609.
Communicated by: Franklin D. Tall
Copyright of article: Copyright 1998, American Mathematical Society

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