2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70781We succeed to say something on the identities of (mu^+, mu) when mu>theta>cf(mu), mu strong limit theta--compact. This hopefully will help to prove the consistency of ``some pair (mu^+,mu) is not compact'', however, this has not been proved.LogicTwo cardinals models with gap one revisitedtext