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Finite unions of equivalence relations

Author(s): John Kittrell
Journal: Proc. Amer. Math. Soc. 136 (2008), 3669-3673.
MSC (2000): Primary 03E15; Secondary 03E20
Posted: May 19, 2008
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Abstract: Say that a class of equivalence relations $ \mathcal{C}$ has the finite union property if every equivalence relation that is the union of finitely many members of $ \mathcal{C}$ must itself be a member of $ \mathcal{C}$. Then the classes of hyperfinite, measure-amenable, Fréchet-amenable, and cheap equivalence relations have the finite union property.

References:

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J. Feldman and C.C. Moore, Ergodic equivalence relations and von Neumann algebras, I, Trans. Amer. Math. Soc. 234 (1977), 289-324. MR 0578656 (58:28261a)

2.
S. Jackson, A.S. Kechris, A. Louveau, Countable Borel equivalence relations, J. Math. Logic 2(1) (2002), 1-80. MR 1900547 (2003f:03066)

3.
A.S. Kechris, B.D. Miller, Topics in orbit equivalence, Springer, 2004. MR 2095154 (2005f:37010)

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Additional Information:

John Kittrell
Affiliation: Knightsbridge Asset Management, LLC, Suite 460, 660 Newport Center Drive, Newport Beach, California 92660
Email: jw.kittrell@gmail.com

DOI: 10.1090/S0002-9939-08-09348-9
PII: S 0002-9939(08)09348-9
Keywords: Countable Borel equivalence relations, hyperfinite equivalence relations, union problems
Received by editor(s): March 26, 2007,
Received by editor(s) in revised form: September 12, 2007
Posted: May 19, 2008
Communicated by: Julia Knight
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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