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High stationarity and derived topologies on $\mathcal{p}_{\kappa}(a)$

M. Catalina Torres
Feb 2024
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摘要原文
Let $\kappa$ be an uncountable regular cardinal, $\kappa \subseteq A$. We study a notion of $n$-stationarity on $\mathcal{P}_{\kappa}(A)$. We construct a sequence of topologies $\langle \tau_0, \tau_1, \dots \rangle $ on $\mathcal{P}_{\kappa}(A)$ characterising the simultaneous reflection of a pair of $n$-stationary sets in terms of elements in the base of $\tau_n$. This result constitutes a complete generalisation to the context of $\mathcal{P}_{\kappa}(A)$ of Bagaria's prior characterisation of $n$-simultaneous reflection in terms of derived topologies on ordinals.
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