# 2015 seminar talk: Uniformization properties in connection to graph colourings

Talk held by Daniel Soukup (Hungarian Academy of Sciences, Budapest, Hungary) at the KGRC seminar on 2015-12-03.

### Abstract

The aim of this talk is to review certain uniformization properties of ladder systems on $\omega_1$. In particular, we focus on a machinery (of iterating a family of simple non proper posets) developed by Shelah investigating the Whitehead problem under CH. Our main interest lies in using this technique to construct uncountably chromatic graphs with interesting/unexpected behavior.