Borel cardinalities below $c_0$
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- by Michael Ray Oliver PDF
- Proc. Amer. Math. Soc. 134 (2006), 2419-2425 Request permission
Abstract:
The Borel cardinality of the quotient of the power set of the natural numbers by the ideal $\mathcal {Z}_0$ of asymptotically zero-density sets is shown to be the same as that of the equivalence relation induced by the classical Banach space $c_0$. We also show that a large collection of ideals introduced by Louveau and Veličkovič, with pairwise incomparable Borel cardinality, are all Borel reducible to $c_0$. This refutes a conjecture of Hjorth and has facilitated further work by Farah.References
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Additional Information
- Michael Ray Oliver
- Affiliation: Department of Mathematics, University of California, Box 951555, Los Angeles, California 90095–1555
- Address at time of publication: Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3
- Email: oliver@cs.ucla.edu
- Received by editor(s): April 5, 2004
- Received by editor(s) in revised form: October 25, 2004, and February 18, 2005
- Published electronically: March 14, 2006
- Communicated by: Carl G. Jockusch, Jr.
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 2419-2425
- MSC (2000): Primary 03E15; Secondary 37A20
- DOI: https://doi.org/10.1090/S0002-9939-06-08207-4
- MathSciNet review: 2213716