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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: 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: 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

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