 Solution

The Lévy reflection theorem says that for every finite collection $\Phi$ of first-order formulas there are arbitrarily large ordinals $\alpha$ such that, for every $\phi \in \Phi$ and every tuple of parameters $a_1,\dots ,a_n\in V_{\alpha }$,Equivalently, the ordinals simultaneously reflecting all formulas in $\Phi$ form a closed unbounded class.

Solved by gpt-5.6-sol high.