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The action of $SL(2,\mathbb{Z} )$ on the subsets of $\mathbb{Z} ^2$

Author(s): Su Gao
Journal: Proc. Amer. Math. Soc. 129 (2001), 1507-1512.
MSC (2000): Primary 03E15, 15A36; Secondary 20A10, 20E05
Posted: October 25, 2000
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Abstract: We prove that the orbit equivalence relation of the canonical action of $SL(2,\mathbb{Z} )$ on the subsets of $\mathbb{Z} ^2$ is a universal countable Borel equivalence relation.

References:

[DJK]
R. DOUGHERTY, S. JACKSON AND A. S. KECHRIS, The structure of hyperfinite Borel equivalence relations, Trans. Amer. Math. Soc. 341 (1994), 193-225. MR 94c:03066

[Hj]
G. HJORTH, Around nonclassifiability for countable torsion free abelian groups, preprint, 1998.

[HK]
G. HJORTH AND A. S. KECHRIS, Borel equivalence relations and classification of countable models, Ann. Pure Appl. Logic 82 (1996), 221-272. MR 99m:03073

[JKL]
S. JACKSON, A. S. KECHRIS AND A. LOUVEAU, Countable Borel equivalence relations, manuscript.

[Ke1]
A. S. KECHRIS, Countable sections for locally compact group actions. II, Proc. Amer. Math. Soc. 120 (1994), 241-247. MR 94b:22004

[Ke2]
A. S. KECHRIS, On the classification problem for rank $2$ torsion-free abelian groups, preprint, 1999.

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Additional Information:

Su Gao
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Email: sugao@its.caltech.edu

DOI: 10.1090/S0002-9939-00-05721-X
PII: S 0002-9939(00)05721-X
Keywords: Borel reducibility, universal countable Borel equivalence relation, free group, free action
Received by editor(s): June 21, 1999
Received by editor(s) in revised form: August 30, 1999
Posted: October 25, 2000
Communicated by: Carl G. Jockusch, Jr.
Copyright of article: Copyright 2000, American Mathematical Society

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