 Solution

The cumulative-hierarchy reflection principle says that for every finite collection $\Phi$ of formulas and every ordinal $\gamma$, there is an ordinal $\alpha >\gamma$ such that for all $\phi \in \Phi$ and all parameters $a_1,\dots ,a_n\in V_{\alpha }$,Equivalently, all quantifiers on the right are relativized to $V_{\alpha }$. It is a theorem schema of ZF for finite lists of formulas, with reflecting stages arbitrarily high. It does not assert one set-sized stage elementary for every formula at once. By beginning above the ranks of any specified finite parameter list, the parameters can also be required to belong to the reflecting stage.