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 | References | Similar Articles | Additional Information

Abstract: The isomorphism and quasi-isomorphism relations on the -local torsion-free abelian groups of rank 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

Email:
scoskey@nylogic.org

DOI:
http://dx.doi.org/10.1090/S0002-9947-2011-05349-3

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.