The classification problem for torsion-free abelian groups of finite rank-Reference-Cited by-同舟云学术

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

Published:2002-10-08 Issue:1 Volume:16 Page:233-258
ISSN:0894-0347
Container-title:Journal of the American Mathematical Society
language:en
Short-container-title:J. Amer. Math. Soc.

Author:

Thomas Simon

Abstract

We prove that for each n ≥ 1 n \geq 1 , the classification problem for torsion-free abelian groups of rank n + 1 n+1 is not Borel reducible to that for torsion-free abelian groups of rank n n .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/jams/2003-16-01/S0894-0347-02-00409-5/S0894-0347-02-00409-5.pdf

Reference35 articles.

1. Trees and amenable equivalence relations;Adams, Scott;Ergodic Theory Dynam. Systems,1990

2. a2 S. Adams, Containment does not imply Borel reducibility, in: S. Thomas (Ed.), Set Theory: The Hajnal Conference, DIMACS Series vol. 58, American Mathematical Society, 2002, pp. 1–23.

3. Linear algebraic groups and countable Borel equivalence relations;Adams, Scot;J. Amer. Math. Soc.,2000

4. Lecture Notes in Mathematics;Arnold, David M.,1982

5. b R. Baer, Abelian groups without elements of finite order, Duke Math. Journal 3 (1937), 68–122.

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