Raphael Carroy (Vienna)

Title: The Open Graph Dichotomy and the second level of the Borel hierarchy

Abstract:

I will sketch a game-theoretical proof of the open graph dichotomy for box-open hypergraphs, and explain how it can be used to obtain various descriptive-set-theoretical dichotomies at the second level of the Borel hierarchy. This shows how to generalise these dichotomies from analytic metric spaces to separable metric spaces by working under the axiom of determinacy.
If time allows it, I will also discuss some connections between cardinal invariants and the chromatic number of the graphs at stake.
This is joint work with Benjamin D. Miller and Daniel T. Soukup.