This is part of a three talk series. The first installment was on June 6, followed by the presentation on June 13.
In the third and final lecture of this series, we will finish outlining the proof of the consistency result that all \(\aleph_n\) can simultaneously carry dense ideals. This will involve a "uniformization" forcing that follows the Shioya collapse, several strategic closure arguments, and lifting an almost-huge embedding. We will focus on the arguments for getting the result on \(\aleph_1\) and \(\aleph_2\), and briefly describe how to modify the uniformization forcing to go further.