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math.LO2023
Torsion-free abelian groups are faithfully Borel complete and pure embeddability is a complete analytic quasi-order
Gianluca Paolini, Saharon Shelah
In [9] we proved that the space of countable torsion-free abelian groups is Borel complete. In this paper we show that our construction from [9] satisfies several additional proper…
math.LO2023
The construction principle and non homogeneity of uncountable relatively free groups
Davide Carolillo, Gianluca Paolini
In [11] Sklinos proved that any uncountable free group is not -homogenenous. This was later generalized by Belegradek in [1] to torsion-free residually finite relatively…
math.LO2023
Anti-Classification Results for Rigidity Conditions in Abelian and Nilpotent Groups
Gianluca Paolini, Saharon Shelah
Relying on the techniques and ideas from our recent paper [13], we prove several anti-classification results for various rigidity conditions in countable abelian and nilpotent grou…