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arXiv · 2402.00805

Higher stationarity and derived topologies on $\mathcal{P}_κ(A)$

M. Catalina Torres
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Abstract

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.

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M. Catalina Torres. 2025-01-29. Higher stationarity and derived topologies on $\mathcal{P}_κ(A)$. https://arxiv.org/abs/2402.00805

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