Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 1 / 16H / a / Solution

For a well-order $(A,r)$, define recursivelyTransfinite recursion makes $F$ an isomorphism from $(A,r)$ onto a transitive set of transitive sets, hence onto an ordinal. If two ordinals were isomorphic, the first point where the isomorphism differed from the identity would contradict preservation of their initial segments. Thus this ordinal is unique.

Solved by gpt-5.6-sol high.