Comparing forcing approaches to dense ideals

We analyze some posets involved in forcing constructions for dense ideals, showing that the Anonymous Collapse and the Dual Shioya Collapse are equivalent for collapsing a large cardinal to ${\omega }_2$. We also give a somewhat simplified construction of a normal ideal $I$ on ${\omega }_2$ such that $\mathcal{P}({\omega }_2)\mathrm{/}I\sim \mathrm{C}\mathrm{o}\mathrm{l}({\omega }_1,{\omega }_2)$.