This will form the first of two interconnected talks on recent work, joint with Nathaniel Bannister and Justin Tatch Moore, showing that it is consistent with the existence of a weakly compact cardinal that strong homology is additive and has compact supports on the class of locally compact separable metric spaces. Together with Mardešić and Prasolov's 1988 consistency result in the opposite direction, this work shows that the aforementioned assertion is independent of the existence of a weakly compact cardinal (by recent refinements, it is even in fact independent of the ZFC axioms). This talk will focus on the bearing of forcing arguments on the higher derived limits lying at the heart of this result.