AI 中文总结
研究$\mathcal{P}_\kappa \lambda$的2 - 平稳性，证明$\kappa$的强紧性不意味着对$\lambda > \kappa$时$\mathcal{P}_\kappa \lambda$是2 - 平稳的，还讨论了相关的Menas定理。
AI 中文摘要
Cody、Lambie - Hanson和Zhang以及Torres引入并研究了$n < \omega$时$\mathcal{P}_\kappa \lambda$的$n$ - 平稳子集概念。他们证明若$\kappa$是超紧的，对所有$\lambda \geq \kappa$及$n < \omega$，$\mathcal{P}_\kappa \lambda$自身是$n$ - 平稳的。本文证明$\kappa$的强紧性并不意味着对$\lambda > \kappa$，$\mathcal{P}_\kappa \lambda$是2 - 平稳的。还讨论了关于$\mathcal{P}_\kappa \lambda$的1 - 平稳和2 - 平稳子集的Menas定理。
英文摘要
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 $\mathcal{P}_κλ$.
Comments27 Pages, Submitted for Publication
