Shelah's pcf boundedness conjecture for inaccessible cardinals

Let ${\mathfrak a}$ be a set of regular cardinals such that every member of ${\mathfrak a}$ is greater than $|{\mathfrak a}|$. Shelah's pcf boundedness conjecture. For no inaccessible cardinal $\lambda$ is $\lambda\cap\operatorname{pcf}({\mathfrak a})$ unbounded in $\lambda$. This is one of the pcf statements presented as lying beyond the methods currently available in the paper.