Additivity of derived limits in the Cohen model

Abstract

We generalize the work of Jeffrey Bergfalk, Michael Hrušák, to show that, in the model constructed by adding sufficiently many Cohen reals, derived limits are additive on a large class of systems. In the process, we isolate a partition principle responsible for the vanishing of derived limits on collections of Cohen reals as well as reframe the propagating trivializations result of [5] as a theorem of ZFC. The results also build on the work of the author, Jeffrey Bergfalk, and Justin Moore [2] to show additvity results for strong homology.