User blog comment:Alemagno12/Beyond countable ordinals/@comment-26428969-20151121173540/@comment-1605058-20151121203159

FA's point is that everything depends on the choice of fundamental sequences for ordinals. We can set $$\omega[n]=Rayo(n)$$ (for example), and then we have $$f_\omega(n)>Rayo(n)$$.