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Strong homology, derived limits, and set theory

Volume 236 / 2017

Jeffrey Bergfalk Fundamenta Mathematicae 236 (2017), 71-82 MSC: Primary 03E75; Secondary 55N40. DOI: 10.4064/fm140-4-2016 Published online: 17 October 2016


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 $\mathbb {R}^4$.


  • Jeffrey BergfalkDepartment of Mathematics
    Cornell University
    Malott Hall
    Ithaca, NY 14853-4201, U.S.A.

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