Open colorings, the continuum and the second uncountable cardinal

Author:
Justin Tatch Moore

Journal:
Proc. Amer. Math. Soc. **130** (2002), 2753-2759

MSC (2000):
Primary 03E65

DOI:
https://doi.org/10.1090/S0002-9939-02-06376-1

Published electronically:
February 12, 2002

MathSciNet review:
1900882

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Abstract | References | Similar Articles | Additional Information

Abstract: The purpose of this article is to analyze the cardinality of the continuum using Ramsey theoretic statements about open colorings or ``open coloring axioms.'' In particular it will be shown that the conjunction of two well-known axioms, and , implies that the size of the continuum is .

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Additional Information

**Justin Tatch Moore**

Affiliation:
Department of Mathematics, Boise State University, Boise, Idaho 83725

Email:
justin@math.boisestate.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06376-1

Keywords:
Open coloring,
OCA,
continuum problem,
oscillation map,
alternation map

Received by editor(s):
March 12, 2001

Received by editor(s) in revised form:
April 11, 2001

Published electronically:
February 12, 2002

Additional Notes:
The research for this paper was supported by EPSRC grant GR/M71121 during the author’s stay at the University of East Anglia; additional support was also received from the Institut Mittag-Leffler during a visit there.

Communicated by:
Alan Dow

Article copyright:
© Copyright 2002
American Mathematical Society