Key points are not available for this paper at this time.
We prove that the Borel space of torsion-free Abelian groups with domain is Borel complete, i. e. , the isomorphism relation on this Borel space is as complicated as possible, as an isomorphism relation. This solves a long-standing open problem in descriptive set theory, which dates back to the seminal paper on Borel reducibility of Friedman and Stanley from 1989.
Paolini et al. (Wed,) studied this question.