User blog comment:Mush9/KING function/@comment-1605058-20170114133107/@comment-1605058-20170114171031

For a very simple reason - they are not of the form \(\alpha+1\) for any \(\alpha\), by definition. You can treat these equally at the expense of shifting in the hierarchy a bit: we can define \[V_\alpha = \bigcup_{\gamma<\alpha}\mathcal P(V_\gamma).\]