Antidiamond principles and topological applications
Authors:
Todd Eisworth and Peter Nyikos
Journal:
Trans. Amer. Math. Soc. 361 (2009), 5695-5719
MSC (2000):
Primary 03E75
DOI:
https://doi.org/10.1090/S0002-9947-09-04705-9
Published electronically:
June 24, 2009
MathSciNet review:
2529910
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We investigate some combinatorial statements that are strong enough to imply that 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:
https://doi.org/10.1090/S0002-9947-09-04705-9
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.