On the Classification Problem for Rank 2 Torsion-free Abelian Groups

  title={On the Classification Problem for Rank 2 Torsion-free Abelian Groups},
  author={Alexander S. Kechris},
We study here some foundational aspects of the classification problem for torsionfree abelian groups of finite rank. These are, up to isomorphism, the subgroups of the additive groups (1n,­), for some n ̄ 1, 2, 3,... . The torsion-free abelian groups of rank% n are the subgroups of (1n,­). For n ̄ 1, that is, the subgroups of (1,­), the isomorphism problem was solved by Baer in the 1930s (see [10]). For every torsion-free abelian group G, x `G, x1 0, and p `P ̄ the set of primes, let 


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