| Résume | In recent years, methods from descriptive set theory have been used to study and classify objects from homological algebra. In this talk, we introduce a hierarchy of complexities for Borel equivalence relations. In particular, we discuss the potential Borel complexity of the isomorphism relation for short exact sequences of countable torsion-free abelian groups. The main tool for this work is the theory of groups with a Polish cover and in particular the notion of Solecki subgroups. We are going to show that, in our context, these are characterized by a certain notion of derivation of a tower. As a result, we find that for a certain class of groups A we can find C such that the classification problem corresponding to Ext(C,A) can have arbitrarily high potential Borel complexity. |
