Nonvanishing Higher Derived Limits without $w\diamondsuit_{ω_1}$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912514200043520 |
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| author | Bannister, Nathaniel |
| author_facet | Bannister, Nathaniel |
| contents | We prove a common refinement of theorems of Bergfalk and of Casarosa and Lambie-Hanson, showing that under certain hypotheses, the higher derived limits of a certain inverse system of abelian groups $\mathbf{A}$ do not vanish. The refined theorem has a number of interesting corollaries, including the nonvanishing of the second derived limit of $\mathbf{A}$ in many of the common models of set theory of the reals and in the Mitchell model. In particular, we disprove a conjecture of Bergfalk, Hrušák, and Lambie-Hanson that higher derived limits of $\mathbf{A}$ vanish in the Miller model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14183 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonvanishing Higher Derived Limits without $w\diamondsuit_{ω_1}$ Bannister, Nathaniel Logic We prove a common refinement of theorems of Bergfalk and of Casarosa and Lambie-Hanson, showing that under certain hypotheses, the higher derived limits of a certain inverse system of abelian groups $\mathbf{A}$ do not vanish. The refined theorem has a number of interesting corollaries, including the nonvanishing of the second derived limit of $\mathbf{A}$ in many of the common models of set theory of the reals and in the Mitchell model. In particular, we disprove a conjecture of Bergfalk, Hrušák, and Lambie-Hanson that higher derived limits of $\mathbf{A}$ vanish in the Miller model. |
| title | Nonvanishing Higher Derived Limits without $w\diamondsuit_{ω_1}$ |
| topic | Logic |
| url | https://arxiv.org/abs/2506.14183 |