Weak Borel chromatic numbers

Given a graph G whose set of vertices is a Polish space X, the weak Borel chromatic number of G is the least size of a family of pairwise disjoint G-independent Borel sets that covers all of X. Here a set of vertices of a graph G is independent if no two vertices in the set are connected by an edge. We show that it is consistent with an arbitrarily large size of the continuum that every closed graph on a Polish space either has a

• Type: Journal
• Year: 2011
• Where: MLQ
• Authors: Stefan Geschke
• Keywords: Borel Chromatic Number, Disjoint G-independent Borel, Machine Learning, MLQ 2011, Polish Space