The computations of strong homology groups of locally compact second countable spaces sometimes involve the computation of higher derived limits of certain inverse systems of abelian groups indexed by $\mathbb{N}^{\mathbb{N}}$. Whether these higher derived limits vanish turns out to be a set-theoretic problem - one which is independent of ZFC by work of Bergfalk and Lambie-Hanson. By recent joint work with Bannister, Bergfalk, and Todorcevic, there is a partition hypothesis which holds in the model of Bergfalk and Lambie-Hanson and which implies the vanishing of these higher derived limits. We also show that the descriptive set theoretic analog of this partition hypothesis is a consequence of the existence of a supercompact cardinal.