If we consider the finitely generated subgroups of F equipped with the embeddability relation, what is the structure of this quasi-order? We will show that this quasi-order contains an increasing well ordered chain of length \(\epsilon_0\), the first fixed point of ordinal exponentiation base \(\omega\). This is joint work with Collin Bleak and Matt Brin.

This talk will be accompanied by a related talk in the logic seminar the same day (2:55pm, 206 Malott). The first talk will focus on group theoretic aspects and motivation; the second talk will provide more details and discuss the set-theoretic aspects of the proof. Each talk may be attended independent of the other.