Geodesic
Strong homology, derived limits, and set theory
Jeffrey Bergfalk 1
1 Department of Mathematics Cornell University Malott Hall Ithaca, NY 14853-4201, U.S.A.
Fundamenta Mathematicae, Tome 236 (2017) no. 1, pp. 71-82 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $\mathbb {R}^4$.
DOI : 10.4064/fm140-4-2016
Keywords: consider question additivity strong homology entails isolating set theoretic content higher derived limits inverse system indexed functions mathbb mathbb system governs certain level additivity strong homology sums arbitrary cardinality addition under assumption proper forcing axiom strong homology additive even closed subspaces mathbb

Jeffrey Bergfalk  1

1 Department of Mathematics Cornell University Malott Hall Ithaca, NY 14853-4201, U.S.A. 
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Jeffrey Bergfalk. Strong homology, derived limits, and set theory. Fundamenta Mathematicae, Tome 236 (2017) no. 1, pp. 71-82. doi: 10.4064/fm140-4-2016

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