A determinacy approach to Borel combinatorics

Creators: Marks, Andrew S.

Abstract

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

Additional Information

© 2015 American Mathematical Society. Received by editor(s): April 12, 2013; Received by editor(s) in revised form: April 29, 2015; Published electronically: June 26, 2015. The author is partially supported by the National Science Foundation under grant DMS-1204907 and the John Templeton foundation under Award No. 15619. The author would also like to thank the Institute for Mathematical Sciences and the Department of Mathematics of the National University of Singapore and the John Templeton Foundation for their support to attend the 2012 summer school in logic, where the main lemma of this paper was conceived. Section 4 of this paper is taken from the author's thesis, which was written under the excellent direction of Ted Slaman. The author would like to thank Professor Slaman for many years of wise advice. The author would also like to thank Clinton Conley, Alekos Kechris, Benjamin Miller, Anush Tserunyan, Robin Tucker-Drob, and Jay Williams for providing helpful feedback and suggestions throughout the development of this paper. Finally, the author would like to thank the referee for many helpful suggestions.

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