 Definable power set

The definable power set $\mathcal{D}(X)=\mathrm{Def}(X)$ consists of the subsets of $X$ definable over the first-order structure $(X,\in )$ by a first-order formula with parameters from $X$. Satisfaction for a set structure makes this a definable operation in ZF. Iterating it produces the constructible hierarchy and the relative constructible hierarchy; their unions are the constructible universe and the relative constructible universe.