Abstract: Milliken’s tree theorem is used to prove that the rationals and the Rado graph have big Ramsey degree. It turns out that there is the complicated dichotomy between coding the halting problem or not based on the size of instance. We will explore what this all means.
This is joint work with Angles d’Auriac, Dzhafarov, Monin, and Patey. This is a companion talk to an earlier talk by Dzhafarov, which was entitled “Milliken’s tree theorem and computability theory.” However, it is not assumed that you have heard the earlier talk.