We will introduce some background and recent progress made in solving the following open problem:

Determine the exact consistency strength of the theory T = ZF + DC + $omega_1$ is supercompact.

It’s known that the upper-bound consistency strength for T is a class of Woodin limits of Woodin cardinals which is (surprisingly) much weaker than ZFC + a supercompact. We will discuss how one might go about computing lower-bounds for T. If time allows, we’ll briefly talk about the relationship of T with the Chang model (CM) and its generalization (CM^+).