A ZFC Dowker space in ℵ_{𝜔+1}: An application of pcf theory to topology

A ZFC Dowker space in $\aleph _{\omega +1}$: An application of pcf theory to topology
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Proc. Amer. Math. Soc. 126 (1998), 2459-2465

DOI: https://doi.org/10.1090/S0002-9939-98-04884-9

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The existence of a Dowker space of cardinality $\aleph _{\omega +1}$ and weight $\aleph _{\omega +1}$ is proved in ZFC using pcf theory.

References

Zoltan T. Balogh, A small Dowker space in ZFC, Proc. Amer. Math. Soc. 124 (1996), no. 8, 2555–2560. MR 1353374, DOI 10.1090/S0002-9939-96-03610-6
Zoltan T. Balogh, A normal screenable nonparacompact space in ZFC, Proc. Amer. Math. Soc. 126 (1998), 1835–1844.
Maxim R. Burke and Menachem Magidor, Shelah’s $\textrm {pcf}$ theory and its applications, Ann. Pure Appl. Logic 50 (1990), no. 3, 207–254. MR 1086455, DOI 10.1016/0168-0072(90)90057-9
C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13
M. Kojman, The A,B,C of pcf: a pcf companion, preprint.
Mary Ellen Rudin, A normal space $X$ for which $X\times I$ is not normal, Fund. Math. 73 (1971/72), no. 2, 179–186. MR 293583, DOI 10.4064/fm-73-2-179-186
Mary Ellen Rudin, Dowker spaces, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 761–780. MR 776636
Saharon Shelah, Cardinal arithmetic, Oxford Logic Guides, vol. 29, The Clarendon Press, Oxford University Press, New York, 1994. Oxford Science Publications. MR 1318912