User blog comment:Ikosarakt1/Ideas of going past psi(K)/@comment-24509095-20140618004924/@comment-5150073-20140618070259

I also don't want to "compute" ordinal $$\alpha$$. I want to compute $$f_\alpha(n)$$, which repeatedly takes fundamental sequence from $$\alpha$$ and reduces it to finite numbers.

And for $$D_\alpha$$, intuition was wrong: it works when $$\alpha$$ is the number. Otherwise, we just take FS for it. FS here is just some sequence of other symbols.