Borel chromatic numbers of closed graphs and forcing with uniform trees

2022/08/14 by Michel Gaspar, Gaspar, Michel, Stefan Geschke +1
Mathematics · Computer Science · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2208.06914

Abstract

In this work, we continue the tradition initiated by Geschke, 2011 of viewing the uncountable Borel chromatic number of analytic graphs as cardinal invariants of the continuum. We show that various uncountable Borel chromatic numbers of closed graphs can be consistently different, as well as consistently equal to the continuum. This is done using arguments that are typical to Axiom A forcing notions.

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