Building Models of Determinacy from Below

We present an $L$-like construction that produces the minimal model of ${\mathsf{A}\mathsf{D}}_{\mathbb{R}}+$“$\mathrm{\Theta }$ is regular”. In fact, our construction can produce any model of ${\mathsf{A}\mathsf{D}}^{+}+{\mathsf{A}\mathsf{D}}_{\mathbb{R}}+V=L(P(\mathbb{R}))$ in which there is no hod mouse with a measurable limit of Woodins.