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Axiomatic set theory course of the University of Oxford

Past exam of the axiomatic set theory course of the University of Oxford

2011

The <cumulative hierarchy> is the <transfinite recursion>
$$
\boxed{V_0=\varnothing,\qquad V_{\alpha+1}=\mathcal P(V_\alpha),\qquad V_\lambda=\bigcup_{\alpha<\lambda}V_\alpha\quad(\lambda\text{ a nonzero limit ordinal}).}
$$
Here $\mathcal P$ is the <power set>. The class $V=\bigcup_{\alpha\in\mathrm{Ord}}V_\alpha$ consists of all sets in <ZF>, by the <Axiom of foundation> and <Axiom schema of replacement>.

Solution

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

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

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