# Publications

47. Essential values of cocycles and the Borel structure of R/Q. Draft.
46. Compositions of periodic automorphisms. Draft.
45. Invariant uniformizations and quasi-transversals. Draft.
44. Edge sliding and transverse hyperfinite decompositions. With Anush Tserunyan. Draft.
43. A dichotomy for countable unions of smooth equivalence relations. With Noé de Rancourt. Submitted.
42. The Feldman-Moore, Glimm-Effros, and Lusin-Novikov theorems over quotients. With Noé de Rancourt. Submitted.
41. Bases for notions of recurrence. With Manuel Inselmann. Submitted.
40. A generalization of the G0 dichotomy and a strengthening of the E3 dichotomy. To appear in the Journal of Mathematical Logic.
39. Scrambled Cantor sets. With Stefan Geschke and Jan Grebík. Proceedings of the American Mathematical Society, 4461-4468, 149 (10), 2021.
38. On the existence of small antichains for definable quasi-orders. With Raphaël Carroy and Zoltán Vidnyánszky. Journal of Mathematical Logic, 2150005, 21 (2), 2021.
37. Recurrence and the existence of invariant measures. With Manuel Inselmann. Journal of Symbolic Logic, 60-76, 86 (1), 2021.
36. Minimal definable graphs of definable chromatic number at least three. With Raphaël Carroy, David Schrittesser, and Zoltán Vidnyánszky. Forum of Mathematics, Sigma, E7 1-16, 9, 2021.
35. On the existence of cocycle-invariant Borel probability measures. Ergodic theory and dynamical systems, 3150-3168, 40 (11), 2020.
34. Bases for functions beyond the first Baire class. With Raphaël Carroy. Journal of Symbolic Logic, 1289-1303, 85 (3), 2020.
33. The open dihypergraph dichotomy and the second level of the Borel hierarchy. With Raphaël Carroy and Dániel Soukup. Contemporary Mathematics, 1-19, 752, 2020.
32. On the existence of large antichains for definable quasi-orders. With Zoltán Vidnyánszky. Journal of Symbolic Logic, 103-108, 85 (1), 2020.
31. Incomparable actions of free groups. With Clinton Conley. Ergodic theory and dynamical systems, 2084-2098, 37 (7), 2017.
30. Sigma-continuity with closed witnesses. With Raphaël Carroy. Fundamenta Mathematicae, 29-42, 239, 2017.
29. Measurable perfect matchings for acyclic locally countable Borel graphs. With Clinton Conley. Journal of Symbolic Logic, 258-271, 82 (1), 2017.
28. Dichotomy theorems for families of non-cofinal essential complexity. With John Clemens and Dominique Lecomte. Advances in Mathematics, 285-299, 304, 2017.
27. Orthogonal measures and strong ergodicity. With Clinton Conley. Israel Journal of Mathematics, 83-89, 218 (1), 2017.
26. Measure reducibility of countable Borel equivalence relations. With Clinton Conley. Annals of Mathematics, 347-402, 185 (2), 2017.
25. A bound on measurable chromatic numbers of locally finite Borel graphs. With Clinton Conley. Mathematical Research Letters, 1633-1644, 23 (6), 2016.
24. The smooth ideal. With Clinton Conley and John Clemens. Proceedings of the London Mathematical Society, 57-80, 112 (1), 2016.
23. An embedding theorem of E0 with model theoretic applications. With Itay Kaplan. Journal of Mathematical Logic, 1450010, 14 (2), 2014.
22. The Borel cardinality of Lascar strong types. With Itay Kaplan and Pierre Simon. Journal of the London Mathematical Society, 609-630, 90 (2), 2014.
21. Essential countability of treeable equivalence relations. With John Clemens and Dominique Lecomte. Advances in Mathematics, 1-31, 265, 2014.
20. An antibasis result for graphs of infinite Borel chromatic number. With Clinton Conley. Proceedings of the American Mathematical Society, 2123-2133, 142 (6), 2014.
19. Stationary probability measures and topological realizations. With Clinton Conley and Alexander Kechris. Israel Journal of Mathematics, 333-345, 198 (1), 2013.
18. Incomparable treeable equivalence relations. Journal of Mathematical Logic, 121-162, 12 (1), 2012.
17. The graph-theoretic approach to descriptive set theory. Bulletin of Symbolic Logic, 554-575, 18 (4), 2012.
16. Definability of small puncture sets. With Andres Caicedo, John Clemens, and Clinton Conley. Fundamenta Mathematicae, 39-51, 215 (1), 2011.
15. Dichotomy theorems for countably infinite dimensional analytic hypergraphs. Annals of Pure and Applied Logic, 561-565, 162 (7), 2011.
14. A classical proof of the Kanovei-Zapletal canonization. Contemporary Mathematics, 281-285, 533, 2011.
13. Descriptive Kakutani equivalence. With Christian Rosendal. Journal of the European Mathematical Society, 179-219, 12 (1), 2010.
12. Ends of graphed equivalence relations, II. With Greg Hjorth. Israel Journal of Mathematics, 393-415, 169, 2009.
11. Ends of graphed equivalence relations, I. Israel Journal of Mathematics, 375-392, 169, 2009.
10. Basis theorems for non-potentially closed sets and graphs of uncountable Borel chromatic number. With Dominique Lecomte. Journal of Mathematical Logic, 121-162, 8 (2), 2008.
9. Measurable chromatic numbers. Journal of Symbolic Logic, 1139-1157, 73 (4), 2008.
8. The existence of quasi-invariant measures of a given cocycle, II: Probability measures. Ergodic Theory and Dynamical Systems, 1615-1633, 28 (5), 2008.
7. The existence of quasi-invariant measures of a given cocycle, I: Atomless, ergodic sigma-finite measures. Ergodic Theory and Dynamical Systems, 1599-1613, 28 (5), 2008.
6. Means on equivalence relations. With Alexander Kechris. Israel Journal of Mathematics, 241-263, 163, 2008.
5. Coordinatewise decomposition of group-valued Borel functions. Fundamenta Mathematicae, 119-126, 196 (2), 2007.
4. Isomorphism of Borel full groups. With Christian Rosendal. Proceedings of the American Mathematical Society, 517-522, 135 (2), 2007.
3. Coordinatewise decomposition, Borel cohomology, and invariant measures. Fundamenta Mathematicae, 81-94, 191 (1), 2006.
2. Full groups, classification, and equivalence relations. PhD Dissertation, 281 pages, 2004.
1. Topics in orbit equivalence. With Alexander Kechris. Lecture Notes in Mathematics, 1852, Springer, 2004.

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