The oscillation stability problem for the Urysohn sphere: A combinatorial approach

Abstract

We study the oscillation stability problem for the Urysohn sphere, an analog of the distortion problem for ${\ell }_2$ in the context of the Urysohn space $\Ur$. In particular, we show that this problem reduces to a purely combinatorial problem involving a family of countable ultrahomogeneous metric spaces with finitely many distances.

19 pages