Logic Seminar

On the classification problem of countable abelian groups

by Dr Martino Lupini (Università di Bologna)

Aula Seminari (Dipartimento di Matematica)

Aula Seminari

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.