On Shelah's Approachability Ideal

Hannes Jakob, Alejandro Poveda

We solve a long-standing open problem of Shelah regarding the \emph{Approachability Ideal} $I[\hat{I}{º}^{+}]$. Given a singular cardinal ${\aleph }_{\hat{I}}^3$, a regular cardinal $μ\in (\mathrm{cf}(…