# Strong colourings over partitions

21.01.2021 15:00 - 17:00

Juris Steprāns (York University, Toronto, Canada)

The celebrated result of Todorcevic that $$\aleph_1\not\rightarrow [\aleph_1]^2_{\aleph_1}$$ provides a well known example of a strong colouring. A mapping $$c:[\omega_1]^2\to \kappa$$ is a strong colouring over a partition $$p:[\omega_1]^2\to \omega$$ if for every uncountable $$X\subseteq \omega_1$$ there is $$n\in \omega$$  such that the range of $$c$$ on $$[X]^2\cap p^{-1}\{n\}$$ is all of $$\kappa$$. I will discuss some recent work with A. Rinot and M. Kojman on negative results concerning strong colourings over partitions and their relation to classical results in this area.

Organiser:

Location:
online via Zoom