Torsion-Free Abelian Groups are Borel Complete

Gianluca Paolini; Saharon Shelah

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arXiv · 2102.12371

Torsion-Free Abelian Groups are Borel Complete

Gianluca Paolini·Saharon Shelah

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Abstract

We prove that the Borel space of torsion-free Abelian groups with domain $\omega$ 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.

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Gianluca Paolini, Saharon Shelah. 2021-02-24. Torsion-Free Abelian Groups are Borel Complete. https://arxiv.org/abs/2102.12371

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