2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59222In this paper we prove that if k is a cardinal in L[0^#], then there is an inner model M such that M |= (V_k,E) has no elementary end extension. In particular if 0^# exists then weak compactness is never downwards absolute. We complement the result with a lemma stating that any cardinal greater than aleph_1 of uncountable cofinality in L[0^#] is Mahlo in every strict inner model of L[0^#].To appear in Proc. of the AMSLogic03E45;03E55text