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arXiv · 2607.16563

On $2$-stationarity of $\mathcal{P}_κλ$

Hiroshi Sakai·M. Catalina Torres
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Abstract

The notion of $n$-stationary subsets of $\mathcal{P}_κλ$ for $n < ω$ were introduced and studied by Cody, Lambie-Hanson \& Zhang \cite{CLHZ} and Torres \cite{T}. They proved that if $κ$ is supercompact, then $\mathcal{P}_κλ$ is $n$-stationary in itself for all cardinals $λ\geq κ$ and all $n < ω$. In this paper we prove that strong compactness of $κ$ does not imply the $2$-stationarity of $\mathcal{P}_κλ$ for cardinals $λ> κ$. We also discuss Menas' Theorem for $1$-stationary and $2$-stationary subsets of $\mathcal{P}_κλ$.

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Hiroshi Sakai, M. Catalina Torres. 2026-07-18. On $2$-stationarity of $\mathcal{P}_κλ$. https://arxiv.org/abs/2607.16563

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