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 \(\aleph_1\).
Ramsey Partitions of Metric Spaces
11.12.2015 15:00 - 16:30
Organiser:
KGRC
Location:
SR 101, 2. St., Währinger Str. 25