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.



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