Logic Seminar

In 2012, Palamourdas claimed that the graph G generated by n commuting Borel functions on a standard Borel space had Borel chromatic number (BCN) at most 2n + 1. In fact, his proof assumed that the functions have no fixed points. In joint work with Palamourdas, we revisit the problem and prove that if every vertex is connected to a fixed point, then there is an increasing filtration {X_i} of the Polish space for which G|X_i has BCN at most 2n for every i.