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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
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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  • [B] R. H. Bing, Metrization of topological spaces, Canad. J. Math. 3 (1951), 175-186. MR 0043449 (13:264f)
  • [DJ] K. Devlin and R. Jensen, Marginalia to a theorem of Silver, ISLIC Logic Conf., Lecture Notes in Math., vol. 499, Springer-Verlag, Berlin and New York, 1975, pp. 115-142. MR 0480036 (58:235)
  • [JD] A. Dodd and R. Jensen, The core model, Ann. Math. Logic 20 (1981), 43-75. MR 611394 (82i:03063)
  • [E] R. Engelking, General topology, Polish Scientific Publishers, Warsaw, 1977. MR 0500780 (58:18316b)
  • [F$ _{1}$] W. G. Fleissner, Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974), 294-298. MR 0362240 (50:14682)
  • [F$ _{2}$] -, A normal, collectionwise Hausdorff, not collectionwise normal space, Topology Appl. 6 (1976), 57-64. MR 0391032 (52:11854)
  • [F$ _{3}$] -, A collectionwise Hausdorff, non normal Moore space with a $ \sigma $-locally countable base, Topology Proc. 4 (1979), 83-96. MR 583690 (81k:54020)
  • [F$ _{4}$] W. G. Fleissner, Normal Moore spaces and large cardinals, Handbook of Set-Theoretic Topology,
  • [Je] T. Jech, Set theory, Academic Press, New York, 1977. (Kunen and Vaughan, Eds.), North-Holland, Amsterdam (to appear). MR 506523 (80a:03062)
  • [J] F. B. Jones, Concerning normal and completely normal spaces, Bull. Amer. Math. Soc. 47 (1937), 671-677. MR 1563615
  • [K] K. Kunen, Set theory: An introduction to independence proofs, North-Holland, New York, 1980. MR 597342 (82f:03001)
  • [M] E. Michael, Point-finite and locally-finite covers, Canad. J. Math. 7 (1955), 275-279. MR 0070147 (16:1138c)
  • [Mt] W. Mitchell, Hypermeasurable cardinals, Studies in Logic 97 (1979), 303-316. MR 567676 (82j:03067)
  • [Na] C. Navy, ParaLindelöf versus paracompact, Topology Appl. (to appear).
  • [N] P. J. Nyikos, A provisional solution to the normal Moore space problem, Proc. Amer. Math. Soc. 78 (1980), 429-435. MR 553389 (81k:54044)
  • [Pr] T. C. Przymusinski, Collectionwise Hausdorff property in product spaces, Colloq. Math. 36 (1976), 49-56. MR 0425895 (54:13845)
  • [T$ _{1}$] F. D. Tall, Set theoretic consistency results and topological theorems, Dissertationes Math. 148 (1977), 1-53. MR 0454913 (56:13156)
  • [T$ _{2}$] -, The normal Moore space problem, Math. Centre Tracts 116 (1979), 243-261. MR 565845 (81f:54016)

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Keywords: Normal Moore space, full sets, large cardinal consistency results
Article copyright: © Copyright 1982 American Mathematical Society

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