Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information


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

References [Enhancements On Off] (What's this?)

  • [B] J. E. Baumgartner, Iterated Forcing, London Mathematical Society Lecture Note Series 87, Cambridge Univ. Press, 1978. MR 87c:03099
  • [D] K. J. Devlin, Constructibility, Springer-Verlag, 1984. MR 85k:03001
  • [E] R. Engelking, General Topology, Helderman Verlag, Berlin, 1989. MR 91c:54001
  • [K] K. Kunen, Set Theory, North Holland, 1980. MR 82f:03001
  • [N] P. Nyikos, A survey of Zero-Dimensional Spaces, Topology (Proc. Nineth Annual Spring Conf., Memphis State Univ., Memphis, Tenn., 1975), pp. 87-114. MR 56:1245
  • [NR] P. J. Nyikos and H. C. Reichel, On the structure of zero-dimensional spaces, Indag. Math. 37 (1975), 120-136. MR 51:1779
  • [P] S. Purisch, The orderability of nonarchimedean spaces, Top. and its Appl. 16 (1983), 273-277. MR 85f:54063
  • [Q] Y. Q. Qiao, On Non-archimedean Spaces, Thesis, Univ. of Toronto, 1992.
  • [QT$_1$] Y. Q. Qiao and F. D. Tall, Perfectly normal non-archimedean spaces in Mitchell models, Top. Proc. 18 (1993), 231-243. MR 96g:54033
  • [QT$_2$] Y. Q. Qiao and F. D. Tall, Perfectly normal non-metrizable non-archimedean spaces are generalized Souslin lines, Proc. Amer. Math. Soc. (to appear).
  • [S] S. Shelah, Proper Forcing, Springer-Verlag Lecture Notes in Mathematics, 940, 1982. MR 84h:03002
  • [ST] S. Shelah and S. B. Todorcevic, A note on the small Baire spaces, Canad. J. Math. 38 no. 3 (1986), 659-665. MR 88c:54005
  • [T$_1$] S. B. Todorcevic, Some consequences of $MA+\neg wKH$, Topology and its Appl. 12 (1981), 203-220. MR 83b:03060
  • [T$_2$] S. B. Todorcevic, Trees, subtrees and order types, Ann. Math. Logic 20 (1981), 233-268. MR 82m:03062

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 03E05, 54E35, 54B05, 54G99, 54A35, 03E45

Retrieve articles in all journals with MSC (1991): 03E05, 54E35, 54B05, 54G99, 54A35, 03E45

Additional Information

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

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

American Mathematical Society