If all Normal Moore Spaces are Metrizable, then there is an Inner Model with a Measurable Cardinal
- 1 September 1982
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 273 (1) , 365-373
- https://doi.org/10.2307/1999211
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.Keywords
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