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arXiv · 1809.00922

Proof of a Conjecture of Galvin

Dilip Raghavan·Stevo Todorcevic
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Abstract

We prove that if the set of unordered pairs of real numbers is colored by finitely many colors, there is a set of reals homeomorphic to the rationals whose pairs have at most two colors. Our proof uses large cardinals and it 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.

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Dilip Raghavan, Stevo Todorcevic. 2018-09-04. Proof of a Conjecture of Galvin. https://doi.org/10.1017/fmp.2020.12

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