If all Normal Moore Spaces are Metrizable, then there is an Inner Model with a Measurable Cardinal

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 Nyik...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 1982, Vol.273 (1), p.365-373
Main Author: Fleissner, William G.
Format: Article
Language:English
Subjects:
Axioms
Cardinality
Cubes
General topology
Large cardinal properties
Mathematical functions
Mathematical set theory
Normal spaces
Topological spaces
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Summary: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.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-1982-0664048-8