On the additivity of strong homology for locally compact separable metric spaces

We show that it is consistent relative to a weakly compact cardinal strong homology additive and compactly supported within the class of locally separable metric spaces. This complements work Mardešić Prasolov [14] showing Continuum Hypothesis implies countable sum Hawaiian earrings witnesses failure possess either these properties. Our results build directly on Lambie-Hanson second author [3] which establishes consistency, cardinal, limsA = 0 for all s ≥ 1 certain pro-abelian group A; we work’s arguments carry implications vanishing additivity lims functors over substantially more general groups indexed by ℕℕ.