Collectionwise normality without large cardinals

Tall, Franklin D.

doi:10.1090/S0002-9939-1982-0647907-7

Collectionwise normality without large cardinals
HTML articles powered by AMS MathViewer

by Franklin D. Tall PDF

Proc. Amer. Math. Soc. 85 (1982), 100-102 Request permission

Abstract:

It was previously known to be consistent relative to a strongly compact cardinal that locally compact perfectly normal spaces must be collectionwise normal. We obtain the same result merely by adjoining ${\aleph _2}$ random reals to a model of $V = L$.

References

Removing the Laver ideal from "Extending Lebesgue measure by countably many sets"

Keith J. Devlin and Saharon Shelah, A note on the normal Moore space conjecture, Canadian J. Math. 31 (1979), no. 2, 241–251. MR 528801, DOI 10.4153/CJM-1979-025-8
William Fleissner, Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974), 294–298. MR 362240, DOI 10.1090/S0002-9939-1974-0362240-4

Handbook of set-theoretic topology

G. Grjunhage, Paracompactness and subparacompactness in perfectly normal locally bicompact spaces, Uspekhi Mat. Nauk 35 (1980), no. 3(213), 44–49 (Russian). International Topology Conference (Moscow State Univ., Moscow, 1979); Translated from the English by A. V. Arhangel′skiĭ. MR 580619
Peter J. Nyikos, A provisional solution to the normal Moore space problem, Proc. Amer. Math. Soc. 78 (1980), no. 3, 429–435. MR 553389, DOI 10.1090/S0002-9939-1980-0553389-4
W. Stephen Watson, Locally compact normal spaces in the constructible universe, Canadian J. Math. 34 (1982), no. 5, 1091–1096. MR 675681, DOI 10.4153/CJM-1982-078-8