First uncountable ordinal of an inner model
= First uncountable ordinal of an inner model
{title2=$\omega_1^M$}
For an <inner model> $M$, the ordinal $\omega_1^M$ is the least ordinal that $M$ regards as uncountable. Equivalently, it is the supremum of the order types of the <well-order code>[well-order codes] belonging to $M$. It can be countable in the ambient universe.