Ulm proved that there is an invariant consisting of a transfinite sequence of integers describing the isomorphism class of each abelian p-group. Hjorth and Kechris proved that these same types of invariants exist for any orbit equivalence relation induced by a continuous action of a Polish group on a Polish space which does not admit a Borel reduction from E_0. This can be interpreted as saying that such equivalence relations are "almost smooth", which we will explore. I will present their result using a different construction called the "Ulm tree", which I believe gives a very intuitive and concrete picture of how these "Ulm-like" invariants arise. I developed this construction in graduate school with the hope of using it along with set-theoretic forcing to prove a strengthening of the Glimm-Effros dichotomy. I will reflect on how this effort was not successful but what could revive those hopes. Along the way I plan to give some insight into how set-theoretic forcing can be used to prove results in descriptive set theory.