# Filippo Calderoni: The bi-embeddability relation for countable abelian groups

Talk held by Filippo Calderoni (Università di Torino, Italy and Politecnico di Torino, Italy) at the KGRC seminar on 2018-04-26.

Abstract: We analyze the Borel complexity of the bi‑embeddability relation for different classes of countable abelian groups. Most notably, we use the Ulm theory to prove that bi‑embeddability is incomparable with isomorphism in the case of p‑groups, and torsion groups. As I will explain, our result contrasts the arguable thesis that the bi‑embeddability relation on countable abelian p‑groups has strictly simpler complete invariants than isomorphism.

This is joint work with Simon Thomas.