Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 128 / 4 / a / 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 $\phi \in \Phi$ and all parameters $\vec{a}\in V_{\alpha }$,Indeed, the ordinals $\alpha$ reflecting all formulas in $\Phi$ form a closed unbounded class.