Filippo Calderoni : The relation of embeddability between torsion-free abelian uncountable groups

Posted by Dima Sinapova , part of the Logic Seminar.

At

March 14, 2017, 4 p.m.

In

SEO 427

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 $\kappa$.