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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Antidiamond principles and topological applications


Authors: Todd Eisworth and Peter Nyikos
Journal: Trans. Amer. Math. Soc. 361 (2009), 5695-5719
MSC (2000): Primary 03E75
Published electronically: June 24, 2009
MathSciNet review: 2529910
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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'skiı 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

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04705-9
PII: S 0002-9947(09)04705-9
Keywords: Diamond, continuum hypothesis, forcing, S-space, P-ideal, antidiamond
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.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.