This is part of a three talk series. The first installment was on June 6 followed by the presentation on June 13.
In the second lecture, we will begin the consistency proof that all \(\omega_n\) can carry dense ideals simultaneously. We start with preliminaries on complete \(\kappa\)-closure, continuous projections, and inverse limits. Then we introduce our main forcing, the Dual Shioya collapse, and establish its key properties.