We prove that if the set of unordered pairs of real numbers is coloured by finitely many colours, there is a set of reals homeomorphic to the rationals whose pairs have at most two colours. Our proof uses large cardinals and verifies a conjecture of Galvin from the 1970s. We extend this result to an essentially optimal class of topological spaces in place of the reals.

中文翻译：

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高尔文猜想的证明

我们证明，如果无序实数对的集合由有限多种颜色着色，则存在一组与有理数同胚的实数，其对最多有两种颜色。我们的证明使用大基数并验证了 1970 年代高尔文的猜想。我们将这个结果扩展到一个基本最优的拓扑空间类来代替实数。