= Solution
Fix $a\in L$. Inside the ambient <transitive model> $M$, the <Axiom of power set> makes the collection of constructible subsets of $a$ a set. For each such subset $x$, choose the least stage of the <constructible hierarchy> at which $x$ appears. The <Axiom schema of replacement> and the <supremum> of a set of <ordinals> give an ordinal $\beta$ bounding all these stages; enlarge $\beta$ so that $a\in L_\beta$.
Now
$$
\mathcal P^L(a)=\{x\in L_\beta:x\subseteq a\}
$$
is definable over $L_\beta$ with parameter $a$. It therefore belongs to the <definable power set> $\mathcal D(L_\beta)=L_{\beta+1}\subseteq L$. This set contains exactly the subsets of $a$ that belong to the <constructible universe>, so it witnesses the <Axiom of power set> in $L$. \b[Therefore $L\models$ Power Set.]
Back to article page
