Past exam of the analytic topology and axiomatic set theory course of the University of Oxford / 2010 / B / 4 / a

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: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.