In recent work with Hayut, we produced a model where for all n > 0, there is a normal ideal $I$ on $\omega_n$ with $P(\omega_n)/I$ forcing equivalent to $Col(\omega_{n-1},\omega_n)$. The most interesting consequences of this stem from a transfer theorem of Woodin that allows us to find copies of boolean algebas of the form $P(\omega_n)/I$ in ones of the form $P(\omega_m)/J$ for $m>n$ and with $J$ uniform and having the same additivity as $I$. We will sketch the proof of Woodin's theorem, raise the question of whether some these transfers can be witnessed by certain surjections that give rise to a direct limit generic ultrapower, and discuss what this could mean for further combinatorial applications.