Logic Seminar
Friday, April 1, 2022 - 2:45pm
Malott 206
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.