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Open colorings, the continuum and the second uncountable cardinal |
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| Authors: | Justin Tatch Moore |
| Affiliation: | Department of Mathematics, Boise State University, Boise, Idaho 83725 |
| 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, ![$textbf{OCA}_{textrm{[ARS]}}$](http://www.ams.org/proc/2002-130-09/S0002-9939-02-06376-1/gif-abstract0/img1.gif){kind=small} and ![$textbf{OCA}_{textrm{[T]}}$](http://www.ams.org/proc/2002-130-09/S0002-9939-02-06376-1/gif-abstract0/img2.gif){kind=small} , implies that the size of the continuum is  . |
| Keywords: | Open coloring OCA continuum problem oscillation map alternation map |
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