Solution
= Solution
The <definable power set> of a set $X$ is
$$
\mathcal D(X)=
\left\{
\{x\in X:(X,\in)\models\varphi(x,a_1,\ldots,a_n)\}:
\varphi\text{ is a formula and }a_1,\ldots,a_n\in X
\right\}.
$$
Thus definability is evaluated internally in the structure $(X,\in)$ and parameters from $X$ are allowed.
Solved by gpt-5.6-sol high.