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A determinacy approach to Borel combinatorics


Author: Andrew S. Marks
Journal: J. Amer. Math. Soc. 29 (2016), 579-600
MSC (2010): Primary 03E15; Secondary 05C15, 05C70, 37A15
DOI: https://doi.org/10.1090/jams/836
Published electronically: June 26, 2015
MathSciNet review: 3454384
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Abstract: We introduce a new method, involving infinite games and Borel determinacy, which we use to answer several well-known questions in Borel combinatorics.


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Additional Information

Andrew S. Marks
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Email: marks@caltech.edu

DOI: https://doi.org/10.1090/jams/836
Received by editor(s): April 12, 2013
Received by editor(s) in revised form: April 29, 2015
Published electronically: June 26, 2015
Additional Notes: 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.
Article copyright: © Copyright 2015 American Mathematical Society