Ramsey ultrafilters and Countable-to-one Uniformization

We show that Countable-to-one Uniformization is preserved by forcing with P(ω)/FinP(ω)/Fin over a model of ZF in which every set of reals is completely Ramsey. We also give an exposition of Todorcevic's theorem that Ramsey ultrafilters are generic for P(ω)/FinP(ω)/Fin over suitable inner models.