Higher stationarity and derived topologies on $\mathcal{P}_κ(A)$
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913670338969600 |
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| author | Torres, M. Catalina |
| author_facet | Torres, M. Catalina |
| contents | Let $κ$ be a regular limit cardinal, $κ\subseteq A$. We study a notion of $n$-s-stationarity on $\mathcal{P}_κ(A)$. We construct a sequence of topologies $\langle τ_0, τ_1, \dots \rangle $ on $\mathcal{P}_κ(A)$ characterising the simultaneous reflection of a pair of $n$-s-stationary sets in terms of elements in the base of $τ_n$. This result constitutes a complete generalisation to the context of $\mathcal{P}_κ(A)$ of Bagaria's prior characterisation of $n$-simultaneous reflection in terms of derived topologies on ordinals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00805 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher stationarity and derived topologies on $\mathcal{P}_κ(A)$ Torres, M. Catalina Logic 03E55, 54G12, 03E02, 03E05 Let $κ$ be a regular limit cardinal, $κ\subseteq A$. We study a notion of $n$-s-stationarity on $\mathcal{P}_κ(A)$. We construct a sequence of topologies $\langle τ_0, τ_1, \dots \rangle $ on $\mathcal{P}_κ(A)$ characterising the simultaneous reflection of a pair of $n$-s-stationary sets in terms of elements in the base of $τ_n$. This result constitutes a complete generalisation to the context of $\mathcal{P}_κ(A)$ of Bagaria's prior characterisation of $n$-simultaneous reflection in terms of derived topologies on ordinals. |
| title | Higher stationarity and derived topologies on $\mathcal{P}_κ(A)$ |
| topic | Logic 03E55, 54G12, 03E02, 03E05 |
| url | https://arxiv.org/abs/2402.00805 |