High dimensional sequential compactness

Abstract

We give examples of $n$-sequentially compact spaces that are not $(n+1)$-sequentially compact under several assumptions. We improve results from Kubis and Szeptycki by building such examples from $\mathfrak{b}=\mathfrak{c}$ and $♢(\mathfrak{b})+\mathfrak{d}={\omega }_1$. We also introduce a new splitting-like cardinal invariant and then show that the same holds under $\mathfrak{s}=\mathfrak{b}$.

29 pages