Torsion-free abelian groups are Borel complete

Gianluca Paolini; Saharon Shelah

doi:10.4007/ANNALS.2024.199.3.4

Torsion-free abelian groups are Borel complete

Gianluca Paolini, Saharon Shelah

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We prove that the Borel space of torsion-free abelian groups with domain ω 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.

Original language	English
Pages (from-to)	1177-1224
Number of pages	48
Journal	Annals of Mathematics
Volume	199
Issue number	3
DOIs	https://doi.org/10.4007/ANNALS.2024.199.3.4
State	Published - 2024

Bibliographical note

Publisher Copyright:
© (2024), Department of Mathematics, Princeton University.

Keywords

Borel completeness
complexity of isomorphism
torsion-free abelian groups

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10.4007/ANNALS.2024.199.3.4

Cite this

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Torsion-free abelian groups are Borel complete

Abstract

Bibliographical note

Keywords

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