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Simultaneously vanishing higher derived limits without large cardinals.
- Source :
-
Journal of Mathematical Logic . Apr2023, Vol. 23 Issue 1, p1-40. 40p. - Publication Year :
- 2023
-
Abstract
- A question dating to Mardešić and Prasolov's 1988 work [S. Mardešić and A. V. Prasolov, Strong homology is not additive, Trans. Amer. Math. Soc. 307(2) (1988) 725–744], and motivating a considerable amount of set theoretic work in the years since, is that of whether it is consistent with the ZFC axioms for the higher derived limits lim n   (n > 0) of a certain inverse system A indexed by ω ω to simultaneously vanish. An equivalent formulation of this question is that of whether it is consistent for all n -coherent families of functions indexed by ω ω to be trivial. In this paper, we prove that, in any forcing extension given by adjoining ℶ ω -many Cohen reals, lim n A vanishes for all n > 0. Our proof involves a detailed combinatorial analysis of the forcing extension and repeated applications of higher-dimensional Δ -system lemmas. This work removes all large cardinal hypotheses from the main result of [J. Bergfalk and C. Lambie-Hanson, Simultaneously vanishing higher derived limits, Forum Math. Pi 9 (2021) e4] and substantially reduces the least value of the continuum known to be compatible with the simultaneous vanishing of lim n A for all n > 0. [ABSTRACT FROM AUTHOR]
- Subjects :
- *COMBINATORICS
*AXIOMS
*MATHEMATICS
*MATHEMATICAL continuum
Subjects
Details
- Language :
- English
- ISSN :
- 02190613
- Volume :
- 23
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Logic
- Publication Type :
- Academic Journal
- Accession number :
- 162754541
- Full Text :
- https://doi.org/10.1142/S0219061322500192