# 2018 seminar talk: New aspects of ladder system uniformization II

Talk held by Daniel Soukup (KGRC) at the KGRC seminar on 2018-12-13.

### Abstract

We continue the previous lecture and present proofs for some of the new results. We show that $\diamondsuit$ implies that for any Aronszajn-tree $T$, there is a ladder system with a 2-colouring with no $T$-uniformization. However, if $\diamondsuit^+$ holds then for any ladder system $\mathbf C$ there is an Aronszajn tree $T$ so that any monochromatic colouring of $\mathbf C$ has a $T$-uniformization.

A video recording of this talk is available on YouTube.