2 problems

Let $(X,f)$ be a finite connectivity system. Its ultrafilter width is … provided that at least one such ultrafilter exists. Connectivity-system SSE-type hardness conjecture. Under…

Let $(X,f)$ be a connectivity system, and let $\mathcal{U}$ be a non-principal ultrafilter of order $k+1$ on $(X,f)$. A majority system of order $k+1$ on $(X,f)$ is a family satisf…