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

Fix an effective coding of machines and write

W_{w}

for the computably enumerable language recognized by code

w

. A set

I

of codes is an index set when membership depends only on the recognized language:

W_{u} = W_{v} ⟹ (u \in I ⟺ v \in I) .

It is nontrivial when it is neither empty nor all of

B

.

Solved by gpt-5.6-sol high.

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