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.
Strong colourings over partitions
21.01.2021 15:00 - 17:00
Organiser:
KGRC
Location:
online via Zoom