Torsion-free abelian groups are Borel complete

• 成果类型: Article
• 署名作者: Paolini, Gianluca; Shelah, Saharon
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2024.199.3.4
• 发表日期: 2024
• 页码: 1177-1224
• 关键词: classification problem

摘要

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 longstanding open problem in descriptive set theory, which dates back to the seminal paper on Borel reducibility of Friedman and Stanley from 1989.