The classification problem for extensions of torsion abelian groups

Martino Lupini

Published 2021-02-06Version 1

Given countable abelian groups $C,A$, with $C$ torsion, we compute the potential complexity class of the classification problem for extensions of $C$ by $A$. In particular, we show that such a problem can have arbitrarily high potential complexity. Toward this goal, we further develop the theory of groups with a Polish cover, in particular by showing that they form an abelian category.