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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Martin's Axiom does not imply perfectly normal non-archimedean spaces are metrizable


Author: Yuan-Qing Qiao
Journal: Proc. Amer. Math. Soc. 129 (2001), 1179-1188
MSC (1991): Primary 03E05, 54E35, 54B05; Secondary 54G99, 54A35, 03E45
Published electronically: November 15, 2000
MathSciNet review: 1610777
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Abstract:

In this paper we prove that in various models of Martin's Axiom there are perfectly normal, non-metrizable non-archimedean spaces of $\aleph_2$.


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Additional Information

Yuan-Qing Qiao
Affiliation: Department of Mathematics, University of Toronto, Toronto, Canada M5S 3G3

DOI: http://dx.doi.org/10.1090/S0002-9939-00-04940-6
PII: S 0002-9939(00)04940-6
Keywords: Non-archmedean, perfect, metrizable, tree base, Martin's Axiom, forcing special tree, $\diamondsuit$, $\square$
Received by editor(s): December 10, 1992
Received by editor(s) in revised form: January 29, 1998
Published electronically: November 15, 2000
Additional Notes: The author’s research was supported by NSERC Grant A-7354
Communicated by: Andreas Blass
Article copyright: © Copyright 2000 American Mathematical Society