 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-1/12i/iv/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

(W_{w})_{w \in W}

K = {w \in W : w \in W_{w}} .

Equivalently, if

f_{w, 1}

is the unary partial function coded by

w

, then

w \in K ⟺ f_{w, 1} (w) ↓ .

Thus $K$ is the diagonal halting set.

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