User blog comment:Ikosarakt1/Ideas of going past psi(K)/@comment-24509095-20140618004924/@comment-5150073-20140618140041

Well, you can treat $$D_D$$ as D-th D-ordinal (or cardinal if you want). The matter is that doesn't change the solution: $$D_D = \sigma(D_{\sigma_{D_{\sigma_{\cdots}}}})$$ and namely that's useful for the FS and Hierarchy.