Torsion-free abelian groups are Borel complete
Copyright policy )Torsion-free abelian groups are Borel complete
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.
- University of Turin Italy
- Rutgers, The State University of New Jersey United States
- Hebrew University of Jerusalem Israel
- Rutgers University New Brunswick United States
Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups, torsion-free abelian groups; Borel completeness; complexity of isomorphism, 03E15, 20K20, 20K30, Mathematics - Logic, Group Theory (math.GR), Torsion-free groups, infinite rank, torsion-free abelian groups, FOS: Mathematics, complexity of isomorphism, Borel completeness, Logic (math.LO), Descriptive set theory, Mathematics - Group Theory
Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups, torsion-free abelian groups; Borel completeness; complexity of isomorphism, 03E15, 20K20, 20K30, Mathematics - Logic, Group Theory (math.GR), Torsion-free groups, infinite rank, torsion-free abelian groups, FOS: Mathematics, complexity of isomorphism, Borel completeness, Logic (math.LO), Descriptive set theory, Mathematics - Group Theory
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