arXiv subjects

M. Catalina Torres

Publications and source records attributed to M. Catalina Torres.

2 recordsLinked to original sources

arXiv2026

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

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 $\mathcal{P}_κλ$.

math.LO↗

arXiv2025

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

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.

math.LO↗