Proof of a Conjecture of Galvin
arXiv:1809.00922 · doi:10.1017/fmp.2020.12
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.
22 pages, Submitted