TITLE: $\kappa$-dense ideals on successor $\kappa$
QUESTION [11 upvotes]: Woodin gave a consistency proof of a normal $\omega_1$-dense ideal on $\omega_1$ from an almost-huge cardinal.  He never published this argument, but it is written up by Foreman in the Handbook of Set Theory.  In this article, and in a paper from the 90s, Foreman claims that this argument is adaptable to other cardinals to yield the consistency of an $\kappa$-dense ideal on $\kappa$ where $\kappa$ is the successor of a regular cardinal.  I have had great trouble trying to prove this claim, as one crucial part of the argument seems specific to $\omega_1$ (which I will explain if you ask).  So does anyone know how to prove Foreman's claim?

REPLY [4 votes]: This is answered in chapter 2 of my thesis.  As far as I know, this is essentially the only method for obtaining such ideals.  I am very interested in finding alternative constructions.  Please contact me if you have some ideas.