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

William G. Fleissner
Transactions of the American Mathematical Society
Vol. 273, No. 1 (Sep., 1982), pp. 365-373
DOI: 10.2307/1999211
Stable URL: http://www.jstor.org/stable/1999211
Page Count: 9
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If all Normal Moore Spaces are Metrizable, then there is an Inner Model with a Measurable Cardinal
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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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