Torsion-Free Abelian Groups are Borel Complete
Logic
2023-02-22 v6 Group Theory
Abstract
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.
Cite
@article{arxiv.2102.12371,
title = {Torsion-Free Abelian Groups are Borel Complete},
author = {Gianluca Paolini and Saharon Shelah},
journal= {arXiv preprint arXiv:2102.12371},
year = {2023}
}