A proof of the Borel completeness of torsion free abelian groups

TL;DR

This paper provides a new proof demonstrating that the classification problem for torsion free abelian groups is Borel complete, indicating maximal complexity in descriptive set theory.

Contribution

It introduces a significantly different proof from previous work, establishing Borel completeness for torsion free abelian groups.

Findings

Proves Borel completeness of torsion free abelian groups

Offers a novel proof approach distinct from prior methods

Enhances understanding of the complexity of classifying such groups

Abstract

A proof of the Borel completeness of torsion free abelian groups is presented. This proof differs considerably from the approach of Paolini-Shelah.