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Open colorings, the continuum and the second uncountable cardinal

Author(s): Justin Tatch Moore
Journal: Proc. Amer. Math. Soc. 130 (2002), 2753-2759.
MSC (2000): Primary 03E65
Posted: February 12, 2002
MathSciNet review: 1900882
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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, $\textbf{OCA}_{\textrm{[ARS]}}$ and $\textbf{OCA}_{\textrm{[T]}}$ , implies that the size of the continuum is $\aleph_2$ .

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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: 10.1090/S0002-9939-02-06376-1
PII: S 0002-9939(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
Posted: 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
Copyright of article: Copyright 2002, American Mathematical Society

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