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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

If all normal Moore spaces are metrizable, then there is an inner model with a measurable cardinal


Author: William G. Fleissner
Journal: Trans. Amer. Math. Soc. 273 (1982), 365-373
MSC: Primary 03E35; Secondary 54A35, 54E30
DOI: https://doi.org/10.1090/S0002-9947-1982-0664048-8
MathSciNet review: 664048
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Abstract: We formulate an axiom, HYP, and from it construct a normal, metacompact, nonmetrizable Moore space. HYP unifies two better known axioms. The Continuum Hypothesis implies HYP; the nonexistence of an inner model with a measurable cardinal implies HYP. As a consequence, it is impossible to replace Nyikos' "provisional" solution to the normal Moore space problem with a solution not involving large cardinals. Finally, we discuss how this space continues a process of lowering the character for normal, not collectionwise normal spaces.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0664048-8
Keywords: Normal Moore space, full sets, large cardinal consistency results
Article copyright: © Copyright 1982 American Mathematical Society