The <definable power set> is
$$
\boxed{\mathcal D(A)=\operatorname{Def}(A,1)
=\left\{\{x\in A:(A,\in)\models\varphi(x,a_1,\ldots,a_n)\}:\varphi\text{ is a first-order formula and }a_1,\ldots,a_n\in A\right\}.}
$$
Thus it contains exactly the <subsets> of $A$ definable over the structure $(A,\in)$ using finitely many parameters from $A$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 121 / 2 / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/iii/paper-121/2/i/solution