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Borel equivalence relations and cardinal algebras

Volume 235 / 2016

Alexander S. Kechris, Henry L. Macdonald Fundamenta Mathematicae 235 (2016), 183-198 MSC: Primary 03E15; Secondary 28A05, 54H05. DOI: 10.4064/fm242-4-2016 Published online: 17 June 2016


We show that Tarski’s concept of cardinal algebra appears naturally in the context of the current theory of Borel equivalence relations. As a result one can apply Tarski’s theory to discover a number of interesting laws governing the structure of Borel equivalence relations, which, in retrospect rather surprisingly, have not been realized before.


  • Alexander S. KechrisDepartment of Mathematics
    California Institute of Technology
    Pasadena, CA 91125, U.S.A.
  • Henry L. MacdonaldMathematics Department
    Occidental College (M-15)
    1600 Campus Rd
    Los Angeles, CA 90041-3314, U.S.A.

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