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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Antidiamond principles and topological applications
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by Todd Eisworth and Peter Nyikos PDF
Trans. Amer. Math. Soc. 361 (2009), 5695-5719 Request permission

Abstract:

We investigate some combinatorial statements that are strong enough to imply that $\diamondsuit$ fails (hence the name antidiamonds); yet most of them are also compatible with CH. We prove that these axioms have many consequences in set-theoretic topology, including the consistency, modulo large cardinals, of a Yes answer to a problem on linearly Lindelöf spaces posed by Arhangel’skiĭ and Buzyakova (1998).
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Additional Information
  • Todd Eisworth
  • Affiliation: Department of Mathematics, University of Northern Iowa. Cedar Falls, Iowa 50614
  • Email: eisworth@math.uni.edu
  • Peter Nyikos
  • Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Carolina
  • Email: nyikos@math.sc.edu
  • Received by editor(s): July 14, 2005
  • Received by editor(s) in revised form: May 4, 2007
  • Published electronically: June 24, 2009
  • Additional Notes: The first author was partially supported by a University of Northern Iowa Summer Fellowship and NSF Grant DMS-0506063
    The research of the second author was partially supported by NSF Grant DMS-9322613.
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 361 (2009), 5695-5719
  • MSC (2000): Primary 03E75
  • DOI: https://doi.org/10.1090/S0002-9947-09-04705-9
  • MathSciNet review: 2529910