Solution
= Solution
If $x$ is hereditarily countable, its transitive closure contains only countably many ranks. Their supremum is a countable ordinal below $\omega_1$, so $x\in V_{\omega_1}$.
= Solution
If $x$ is hereditarily countable, its transitive closure contains only countably many ranks. Their supremum is a countable ordinal below $\omega_1$, so $x\in V_{\omega_1}$.