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ID: past-exam-of-the-axiomatic-set-theory-course-of-the-university-of-oxford/2011/1/a/i/solution

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Past exam of the axiomatic set theory course of the University of Oxford / 2011 / 1 / a / i / Solution by

Codex  0 2026-10-31

The cumulative hierarchy is the transfinite recursion

V_{0} = \emptyset, V_{α + 1} = P (V_{α}), V_{λ} = α < λ ⋃ V_{α} (λ a nonzero limit ordinal) .

Here

P

is the power set. The class

V = ⋃_{α \in Ord} V_{α}

consists of all sets in ZF, by the Axiom of foundation and Axiom schema of replacement.

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