## 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