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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

The classification problem for torsion-free abelian groups of finite rank


Author: Simon Thomas
Journal: J. Amer. Math. Soc. 16 (2003), 233-258
MSC (2000): Primary 03E15, 20K15, 37A20
Published electronically: October 8, 2002
MathSciNet review: 1937205
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Abstract: We prove that for each $n \geq 1$, the classification problem for torsion-free abelian groups of rank $n+1$ is not Borel reducible to that for torsion-free abelian groups of rank $n$.


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Additional Information

Simon Thomas
Affiliation: Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019
Email: sthomas@math.rutgers.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-02-00409-5
PII: S 0894-0347(02)00409-5
Keywords: Borel equivalence relation, torsion-free abelian group, superrigidity
Received by editor(s): March 1, 2001
Received by editor(s) in revised form: September 25, 2002
Published electronically: October 8, 2002
Additional Notes: Research partially supported by NSF Grants.
Article copyright: © Copyright 2002 American Mathematical Society