An antibasis result for graphs of infinite Borel chromatic number

Clinton T. Conley, Benjamin D. Miller
2014 Proceedings of the American Mathematical Society  
We answer in the negative a question posed by Kechris-Solecki-Todorcevic as to whether the shift graph on Baire space is minimal among graphs of indecomposably infinite Borel chromatic number. To do so, we use ergodic-theoretic techniques to construct a new graph amalgamating various properties of the shift actions of free groups. The resulting graph is incomparable with any graph induced by a function. We then generalize this construction and collect some of its useful properties. 2010
more » ... rties. 2010 Mathematics Subject Classification. Primary 03E15; secondary 28A05, 37A20.
doi:10.1090/s0002-9939-2014-11918-6 fatcat:dxh77lcrd5gelacraxl5e5cf6e