Solution (source code)

= Solution

The <Lévy reflection theorem> states that for every finite collection $\Phi$ of formulas and every ordinal $\gamma$, there is an ordinal $\alpha>\gamma$ such that, for every $\varphi\in\Phi$ and all parameters $\vec a\in V_\alpha$,
$$
\boxed{V\models\varphi(\vec a)\iff V_\alpha\models\varphi(\vec a).}
$$
Indeed, the ordinals $\alpha$ reflecting all formulas in $\Phi$ form a closed unbounded class.