## Logic Seminar

Filippo Calderoni

Università di Torino

The relation of embeddability between torsion-free abelian uncountable groups

**Abstract:**We will discuss the problem of determining the Borel complexity of the analytic quasi-order of embeddability between torsion-free abelian groups in both the settings of the classical and generalized Descriptive Set Theory. Then we will see how we can slightly modify a categorical construction by Przezdziecki to prove that, for every uncountable $\kappa$ such that $\kappa^{<\kappa}=\kappa$, the embeddability between $\kappa$-sized torsion-free abelian groups is as complicated as possible among the analytic quasi-orders defined on the generalized Baire space on $\kappa$.

Tuesday March 14, 2017 at 4:00 PM in SEO 427