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The classification of torsion-free abelian groups of finite rank up to isomorphism and up to quasi-isomorphism

Author: Samuel Coskey
Journal: Trans. Amer. Math. Soc. 364 (2012), 175-194
MSC (2010): Primary 03E15; Secondary 20K15
Published electronically: August 31, 2011
MathSciNet review: 2833581
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Abstract: The isomorphism and quasi-isomorphism relations on the $ p$-local torsion-free abelian groups of rank $ n\geq3$ are incomparable with respect to Borel reducibility.

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Additional Information

Samuel Coskey
Affiliation: Mathematics Program, The Graduate Center of The City University of New York, 365 Fifth Avenue, New York, New York 10016
Address at time of publication: York University and The Fields Institute, 222 College Street, Toronto, Ontario, Canada M5S 2N2

Keywords: Countable Borel equivalence relations, torsion-free abelian groups, superrigidity
Received by editor(s): February 6, 2009
Received by editor(s) in revised form: March 16, 2010
Published electronically: August 31, 2011
Additional Notes: This is a part of the author’s doctoral thesis, which was written under the supervision of Simon Thomas. This work was partially supported by NSF grant DMS 0600940.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.