2015 seminar talk: Ramsey Partitions of Metric Spaces

Talk held by Jonathan Verner (Charles University in Prague, Czech Republic) at the KGRC seminar on 2015-12-11.

Abstract

We investigate the existence of metric spaces which, for any coloring with a fixed number of colors, contain monochromatic isomorphic copies of a fixed starting space $K$. I shall present a proof, due to Shelah, that for colorings with $\kappa$ colors and a $K$ of size $\kappa$ such a space can always be found of size $2^\kappa$. Time permitting I will also present a slightly weaker theorem for countable ultrametric $K$ where, however, the resulting space has size $\aleph_1$.