Comment by Gro-Tsen on What is the least $\alpha$ such that $L_\alpha$ contains a non-measurable set

Just to be clear, you answered the question “what is the smallest $α$ such that $L_α$ contains a subset of $2^ω$ which is not measurable in the universe ($V=L$)?”; another possible interpretation of the (to me ambiguous) question might have been “what is the smallest $α$ such that $L_α$ $\vDash$ «there exists a subset of $2^ω$ which is not measurable»?”. I don't know what can be said about the latter $α$, but it is obviously countable.