Strong homology, derived limits, and set theory
Volume 236 / 2017
Fundamenta Mathematicae 236 (2017), 71-82
MSC: Primary 03E75; Secondary 55N40.
DOI: 10.4064/fm140-4-2016
Published online: 17 October 2016
Abstract
We consider the question of the additivity of strong homology. This entails isolating the set-theoretic content of the higher derived limits of an inverse system indexed by the functions from $\mathbb {N}$ to $\mathbb {N}$. We show that this system governs, at a certain level, the additivity of strong homology over sums of arbitrary cardinality. We show in addition that, under the assumption of the Proper Forcing Axiom, strong homology is not additive, not even on closed subspaces of $\mathbb {R}^4$.
