Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 1 / 12F / b / Solution

Let $K=\{w:w\in W_w\}$ and let $e_{\varnothing }$ be any index for the empty language. The proof of Rice theorem givesIn either case choose a language on the opposite side of the nontrivial property and switch from the empty enumerator to its enumerator if the simulated diagonal computation halts.