 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-3/12j/e/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

g_{0}

e

would satisfy

W_{e} = W_{j}

when

e \in Inf

and

W_{e} = W_{i}

when

e \in Fin

, a contradiction in either case. The same argument applies to

g_{1}

. A total recursive reduction

h

with

n \in Inf ⟺ h (n) \in Fin

would provide such a forbidden switch (and would collapse the known distinct arithmetical complexities), so none exists.

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