User blog comment:Ikosarakt1/Fast-growing hierarchy/@comment-7484840-20130620190007/@comment-5150073-20130620191806

It is okay for first 3 rules, the 4rd is wrong: since theta(w,w)[n] ≠ theta(n,n). 6th is problematic again: say, theta(w,1)[n] ≠ theta(w[n],1) = theta(n,1) (which is much smaller).

7th and 9th are trying to define [n] for the first uncountable ordinal, which is impossible by its definition.

Also, you don't described the conditions for rules.