2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224935We generalize to the relations $(λ, μ) \stackrelκ{\Rightarrow} (λ', μ')$ and $\alm (λ, μ) \stackrelκ{\Rightarrow} \alm (λ', μ')$ some results obtained in Parts II and IV. We also present a multi-cardinal version.11 pagesLogic03C20, 03E05, 03C95; 03C55, 03C98Combinatorial and model-theoretical principles related to regularity of ultrafilters and compactness of topological spaces. Vtext