A determinacy approach to Borel combinatorics

Abstract

We introduce a new method, involving infinite games and Borel determinacy, which we use to answer several well-known questions in Borel combinatorics.

Minor corrections and some reorganization of section 4

References in corpus (2)

• Limits of local-global convergent graph sequences
• Brooks's theorem for measurable colorings

Cited by in corpus (14)

• Baire measurable paradoxical decompositions via matchings
• Continuous Combinatorics of Abelian Group Actions
• Brooks's theorem for measurable colorings
• Distributed Algorithms, the Lovász Local Lemma, and Descriptive Combinatorics
• Borel Edge Colorings for Finite Dimensional Groups
• On Homomorphism Graphs
• The measurable Hall theorem fails for treeings
• Minimal definable graphs of definable chromatic number at least three
• Uniformity, Universality, and Computability Theory
• Measurable perfect matchings for acyclic locally countable Borel graphs
• Borel Vizing's Theorem for 2-Ended Groups
• Equitable Colorings of Borel Graphs
• Borel structurability on the 2-shift of a countable group
• Complexity of Finite Borel Asymptotic Dimension