Open colorings, the continuum and the second uncountable cardinal

Moore, Justin

doi:10.1090/S0002-9939-02-06376-1

Open colorings, the continuum and the second uncountable cardinal
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Proc. Amer. Math. Soc. 130 (2002), 2753-2759 Request permission

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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