The <constructible hierarchy> is defined by transfinite recursion:
$$
L_0=\varnothing,
\qquad
L_{\beta+1}=\mathcal D(L_\beta),
\qquad
L_\lambda=\bigcup_{\beta<\lambda}L_\beta
$$
when $\lambda$ is a <limit ordinal>. Its union over all ordinals is the constructible universe $L$.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 128 / 1 / a / ii / Solution

{title2=$L_\alpha$}
{wiki=Constructible_universe}

The constructible hierarchy is defined by
$$
L_0=\varnothing,
\qquad L_{\alpha+1}=\mathcal D(L_\alpha),
\qquad L_\lambda=\bigcup_{\alpha<\lambda}L_\alpha
$$
for limit ordinals $\lambda$. Its union is the constructible universe $L$.

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