J an K ruschewski . Inner Model Theory and Kripke–Platek Set Theory . Universität Münster. 2025. Supervised by Farmer Schlutzenberg. MSC: Primary 03E45, Secondary 03E55, 03D60. Keywords: inner model theory, admissibility, mouse, Kripke–Platek set theory, constructibility, HOD, set-theoretic geology, Woodin cardinal, determinacy.

The thesis is thematically divided into three parts. Part I investigates the following conjecture of John Steel from “The Core Model Iterability Problem”: Conjecture (ZFC). Let Ω Ω normal upper Omega be a measurable cardinal and R R script upper R and W W script upper W be premice such that OR R = OR W = Ω ORR = ORW = Ω upper O upper R Superscript script upper R Baseline equals upper O upper R Superscript script upper W Baseline equals normal upper Omega and both are ( 0 , Ω + 1 ) (0,Ω +1) left parenthesis 0 comma normal upper Omega plus 1 right parenthesis -iterable. Then the following are equivalent : $:$ colon 1. W ≤ ∗