Alexander Kechris

Professor Alexander Kechris is Professor of Mathematics (Emeritus) at Caltech. He has made extensive contributions to the definability theory of the continuum and its connections and applications to classical and harmonic analysis, ergodic theory, topological dynamics, combinatorics, computability theory and model theory.

Selected Publications

• (with T. Arant and P. Lutz) Borel graphable equivalence relations, Advances in Mathematics, 487 (2026), 110765. Click here for the online version
• Definable cardinality, preprint, 2025. Click here for the .pdf file
• The Theory of Countable Borel Equivalence Relations, Cambridge University Press, 2025.
• (with M. Wolman) Invariant uniformization, preprint 2024. Click here for the arXiv
• The spaces of measure preserving equivalence relations and graphs, preprint 2024. Click here for the .pdf file
• (with M. Wolman) Ditzen's effective version of Nadkarni's Theorem, preprint 2024. Click here for the .pdf file
• (with J. Frisch,  F. Shinko and Z. Vidnyánszky) Realizations of countable Borel equivalence relations, preprint, to appear in Memoirs Amer. Math. Soc. Click here for the arXiv
• The theory of countable Borel equivalence relations. This material has been published by Cambridge University Press as "The theory of countable Borel equivalence relations" by Alexander S. Kechris. This pre-publication version is free to view and download for personal use only. Not for re-distribution, re-sale or use in derivative works. © Alexander S. Kechris 2024. Click here for the .pdf file
• (with J. Frisch and F. Shinko) Lifts of Borel actions on quotient spaces, Israel J. Math., special volume for Benjamin Weiss, 251 (2022), 379-421. Click here for the Sharedit
• (with M. Malicki, A. Panagiotopoulos and J. Zielinski) On Polish groups admitting non-essentially countable actions, Erg. Theory and Dynam. Systems, 42 (2022), 180--194. Click here for the .pdf file 
• Global aspects of measure preserving equivalence relations and graphs, New Zealand Journal of Math., Vaughan Jones Memorial Issue, 52 (2021), 691-726. Click here for the .pdf file
• (Co-edited with N. Makarov, D. Ramakrishnan and X. Zhu) Nine Mathematical Challenges: An Elucidation, Proc. of Symp. in Pure Math., 104, American Mathematical Society, 2021.
• (Co-edited with B. Loewe and J.R. Steel), Large cardinals, determinacy and other topics, Lecture Notes in Logic 49, Cambridge University Press, 2021.
• Quasi-invariant measures for continuous group actions, Trends in Set Theory, Ed. by S. Coskey and G. Sargsyan, Contemp. Math., 752 (2020), 113-120. Click here for the .pdf file 
• (with P.J. Burton) Weak containment of measure preserving group actions, Erg. Theory and Dynam. Systems, 40, (2020), 2681--2733. Click here for the .pdf file
• (with A.S. Marks) Descriptive graph combinatorics, preprint, 2020. Click here for the .pdf file
• (with V. Quorning) Co-induction and invariant random subgroups, Groups, Geometry, and Dynamics, 13(4) (2019), 1151--1193. Click here for the arXiv 
• (with R. Chen) Structurable equivalence relations, Fund. Math., 242 (2018), 109--185. Click here for the .pdf file. arXiv expanded version arXiv
• (with A. Nies and K. Tent) The complexity of topological group isomorphism,J. Symb. Logic, 83(3) (2018), 1190--1203. Click here for the .pdf file
• (with P. J. Burton ) Invariant random subgroups and action versus represe ntation maximality, Proc. Amer. Math. Soc., 145(9) (2017), 3961--3971. Click here for arXiv
• (with M. Sokic and S. Todorcevic) Ramsey properties of finite measure algebras and topological dynamics of the group of measure preserving automorphisms: some results and an open problem, in: Foundations of Mathematics, Essays in Honor of W. Hugh Woodin's 60th Birthday, Ed. by A.E. Caicedo et al., Contemp. Math., 690 (2017), 69-85,  Click here for the .pdf file
• (Co-edited with B. Loewe and J.R. Steel), Ordinal Definability and Recursion Theory: The Cabal Seminar, Volume III, Lecture Notes in Logic 43, Cambridge University Press, 2016.
• (with D. A. Martin) On the theory of $\Pi^1_3$ sets of reals, II , in:  Ordinal Definability and Recursion Theory:  The Cabal Seminar, Volume III, Lecture Notes in Logic 43, Cambridge University Press, 2016, 200-219.
• (with H.L. Macdonald) Borel equivalence relations and cardinal algebras, Fund. Math., 235 (2016),  183--198. Click here for the .pdf file | Corrections: .pdf file
• In memoriam:  Gregory Hjorth (1963-2011), Bulletin of Symbolic Logic 17(3) (2011), 471-477. | Corrections: .pdf file
• Global aspects of ergodic group actions, Mathematical Surveys and Monographs, 160, American Mathematical Society, 2010. | Corrections and Updates: .pdf file
• (with B.D. Miller) Topics in Orbit Equivalence, Lecture Notes in Mathematics, Springer, Vol. 1852, 2004
  • A typical reader's reaction to the book
  • Corrections and Updates: Click here for the .pdf file
• Set theory and uniqueness for trigonometric series , preprint, 1997.  Click here for the .pdf file
• (with H. Becker) The Descriptive Set Theory of Polish Group Actions , London Math. Soc. Lecture Note Series, 232, Cambridge University Press, 1996. | Corrections and Updates: click here for the .pdf file
• Classical Descriptive Set Theory, Graduate Texts in Mathematics, 156, Springer, 1995. | Corrections and Updates: Click here for the .pdf file

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RTG Logic Meetings at Caltech

• Logic in Southern California 2015-16: Februrary 20, 2016
• Logic in Southern California 2014-15: March 7, 2015
• Logic in Southern California 2013-14: March 8, 2014
• Logic in Southern California 2012-13: November 17, 2012
• Logic in Southern California 2011-2012: February 18, 2012