On Shelah's Approachability Ideal

Hannes Jakob, Alejandro Poveda

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