On the classification problem of countable abelian groups
(Università di Bologna)
Aula Seminari (Dipartimento di Matematica)
Dipartimento di Matematica
I will present the framework of Borel-definable homological algebra, where classical constructions and invariants from homological algebra are enriched with additional information of descriptive set-theoretic nature. I will then explain how this viewpoint allows us to study the complexity of the problem of classifying extensions of two given countable abelian groups, and how the techniques of Borel-definable homological algebra can be also used to obtain new purely algebraic results.