Logic Seminar

Justin MooreCornell University
A descriptive approach to higher derived limits

Friday, November 18, 2022 - 2:45pm
Malott 206

It is known that the computation of strong homology groups of locally compact second countable spaces reduces to the computation of higher derived limits of inverse systems of abelian groups indexed by $\omega^\omega$. The computation of these higher derived limits is facilitated in part by a Ramsey-theoretic partition hypothesis. In general this partition hypothesis can be forced starting from a suitable large cardinal assumption. We show that if one places regularity assumptions on cells in the partition, then the conclusion of the partition hypothesis followed directly from a large cardinal hypothesis. This points to the possibility of a variant of strong homology whose properties are less sensitive to set theoretic assumptions.