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math.GR2021★ 1 cited
On the existence of uncountable Hopfian and co-Hopfian abelian groups
Gianluca Paolini, Saharon Shelah
We deal with the problem of existence of uncountable co-Hopfian abelian groups and (absolute) Hopfian abelian groups. Firstly, we prove that there are no co-Hopfian reduced abelian…
math.LO2021★ 3 cited
Torsion-Free Abelian Groups are Borel Complete
Gianluca Paolini, Saharon Shelah
We prove that the Borel space of torsion-free Abelian groups with domain is Borel complete, i.e., the isomorphism relation on this Borel space is as complicated as possible, as…