This is a continuation of the KGRC Set Theory seminar talk I gave in June 2021. I will quickly repeat the content of the first talk and focus on things I did not cover then. It is well known that the (universal countable) Rado graph has finite big Ramsey degrees. I.e., given a finite colouring of n-tuples of its vertices there is a copy of the Rado graph such that its n-tuples have at most D(n)-many colours. The proof of this fact uses a theorem of Milliken for trees. I will talk about the extension of this argument which works also for universal structures with higher arities, in particular 3-uniform hypergraphs.
Joint work with M. Balko, J. Hubička, M. Konečný, and L. Vena, see https://arxiv.org/abs/2008.00268
Please note that the Zoom meeting ID and passcode change for the Set Theory Seminar starting with this talk (but remain unchanged for other KGRC seminars).