2021/07/08 by Boban Veličković, Velickovic, Boban, Alessandro Vignati +1 · 3 citations
Arts and Humanities · Computer Science · Mathematics · #03E35 #03E75 #18E25 #55Nxx #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #Logic (math.LO) #Philosophy and History of Science #Topological and Geometric Data Analysis
paper · doi:10.48550/arxiv.2107.03787
openalex publication_date 2021/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the study of strong homology Mardešić and Prasolov isolated a certain inverse system of abelian groups \mathbf A indexed by elements of ωω. They showed that if strong homology is additive on a class of spaces containing closed subsets of Euclidean spaces then the higher derived limits limn \mathbf A must vanish, for n>0. They also proved that under the Continuum Hypothesis lim1 \mathbf A ≠ 0. The question whether limn \mathbf A vanishes, for n>0, has attracted considerable interest from set theorists. Dow, Simon and Vaughan showed that under PFA lim1 \mathbf A =0. Bergfalk show that it is consistent that lim2\mathbf A does not vanish. Later Bergfalk and Lambie-Hanson showed that, modulo a weakly compact cardinal, it is relatively consistent with ZFC that limn \mathbf A =0, for all n. The large cardinal assumption was recently removed by Bergfalk, Hrušak and Lambie-Henson. We complete the picture by showing that, for any n>0, it is relatively consistent with ZFC that limn \mathbf A ≠ 0.