= Absoluteness of constructible levels
{title2=$L_\alpha^M=L_\alpha$}
For a <transitive model> $M$ of <ZFC> and $\alpha\in M\cap\operatorname{Ord}$, the internally computed <constructible hierarchy> agrees with the ambient level: $L_\alpha^M=L_\alpha$. Satisfaction for a fixed set structure is computed from the same finite formulas and the same domain in both universes. <Transfinite recursion> then proves agreement at successors and limits. If $\theta=M\cap\operatorname{Ord}$, it follows that $L_\theta\subseteq M$.
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