Analytic digraphs of uncountable Borel chromatic number under injective definable homomorphism

Abstract: We study the analytic digraphs of uncountable Borel chromatic number on Polish spaces, and compare them with the notion of injective Borel homomorphism. We provide some minimal digraphs incomparable with G 0. We also prove the existence of antichains of size continuum, and that there is no finite basis. 2010 Mathematics Subject Classification. 03E15, 54H05