LFCS Seminar: Tuesday, 9 April - Joanna Boyland

Title:      Big Ramsey Degrees of Countable Ordinals            

Abstract:

Ramsey's theorem on infinite sets states that for all natural numbers $n$, for all finite colorings of the $n$-element subsets of some infinite set, there exists an infinite monochromatic subset. If we also wish the subset to share some structural properties with the original set, this is not always possible. However, sometimes you can guarantee the existence of a subset that has only $t$ colors, for some constant integer $t$ that depends on the original set. We will discuss how to find this $t$, the Big Ramsey Degree, for various examples, and describe briefly the results of the paper, which found the exact Big Ramsey Degrees of all ordinals under $\omega^\omega$, degrees which were shown to be finite by Mašulović and Šobot (2021).