Hod Mice and the Mouse Set Conjecture

The author develops the theory of Hod mice below $AD_{\mathbb{R}}+$ ``$\Theta$ is regular''. He uses this theory to show that HOD of the minimal model of $AD_{\mathbb{R}}+$ ``$\Theta$ is regular'' satisfies $GCH$. Moreover, he shows that the Mouse Set Conjecture is true in the minimal model of $AD_{\mathbb{R}}+$ ``$\Theta$ is regular''.