User blog comment:Scorcher007/Analysis DAN up to Z2/@comment-27513631-20180829075155

\(L_\alpha\prec_2 L_{\alpha+1}\), the incorrect definition of 2-stable you gave, is never true.

If \(\alpha\) is a limit, \(\exists \alpha(\text{Ord}(\alpha)\land\forall\beta(\text{Ord}\beta\to\beta\subseteq\alpha\) is true in one but not the other.

If \(\alpha\) is a successor, then \(L_\alpha\prec_1 L_{\alpha+1}\) can't even hold.