 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-4/16h/e/solution

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

φ

s_{V} = {z \in x : V ⊨ φ (z)},

(M, \in)

requires

s_{M} = {z \in x : M ⊨ φ (z)} .

An arbitrary formula need not be absolute between a transitive class and the ambient universe, so

s_{V}

and

s_{M}

can differ. Closure under

s_{V}

therefore supplies no reason for the required set

s_{M}

to belong to

M

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