2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141462The Inner Model Hypothesis (IMH) and the Strong Inner Model Hypothesis (SIMH) were introduced by the first author in ``Internal consistency and the inner model hypothesis'', Bulletin of Symbolic Logic, December 2006. In this article we establish some upper and lower bounds for their consistency strength.14 pagesLogic03E35, 03E45, 03E65, 03E55,03E60text