= Solution
For a set $A$, its <definable power set> consists of the subsets of $A$ definable by a <first-order formula> over $(A,\in)$ using finitely many parameters from $A$. The quantifiers range over $A$; this is generally much smaller than its full <power set>.
The <constructible universe> is defined by <transfinite recursion>:
$$
\boxed{L_0=\varnothing,\qquad L_{\alpha+1}=\operatorname{Def}(L_\alpha),\qquad
L_\lambda=\bigcup_{\alpha<\lambda}L_\alpha\quad(\lambda\text{ a limit ordinal}),\qquad
L=\bigcup_{\alpha\in\mathrm{On}}L_\alpha.}
$$
The last <union> denotes a definable <proper class>, not a set-sized <union> over a set of all <ordinals>. At a successor stage, only definitions over the previously constructed stage are permitted.
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