### Weakly compact **Def.** $\kappa \to(\kappa,\kappa)^2$ ![[Infinite combinatorics#^103037]] ### $O^k$ O-kukri **Def**. There exists an elementary embedding of an inner model with a proper class of measurable cardinals to itself. **Def.** Let $O^k$ name $M_0$ being the least (with respect to the mouse ordering) sound active mouse of the form $M_0 =_{df} \langle J_{α_0}^{E^{M_0}} , E^{M_0} , F_0 \rangle$ so that $M_0 \vDash$ “$F_0$ is a normal measure on $\tau_0 ∧ ∀ \delta < \tau_0 ∃\lambda < \tau_0$($\delta < \lambda ∧ \lambda$ is a measurable cardinal)”.