Series: Penn State Logic Seminar

Date: Thursday, November 29, 2001

Time: 9:45 - 11:00 AM

Place: 169 Willard Building

Speaker: Simon Thomas, Mathematics, Rutgers University

Title: The Classification Problem for Torsion-Free Abelian Groups of
       Finite Rank


In 1937, Baer introduced the notion of the type of an element in a
torsion-free abelian group and showed that this notion provided a
complete invariant for the classification problem for the torsion-free
abelian groups of rank 1. In this talk, I will discuss some recent
contributions to the project of explaining why no satisfactory system
of complete invariants has yet been found for the torsion-free abelian
groups of finite rank n > 1. The talk will include a discussion of
where this classification problem is situated within the descriptive
set-theoretic context of countable Borel equivalence relations.