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.
Torsion-free abelian groups are Borel complete
Paolini G.
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2024-01-01
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 longstanding 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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