Proof of a Conjecture of Galvin
Logic
2020-12-23 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.1809.00922,
title = {Proof of a Conjecture of Galvin},
author = {Dilip Raghavan and Stevo Todorcevic},
journal= {arXiv preprint arXiv:1809.00922},
year = {2020}
}
Comments
22 pages, Submitted