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 | |
| 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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