User blog comment:Ikosarakt1/Fast-growing hierarchy/@comment-157.193.1.38-20130622201600/@comment-157.193.53.9-20130627190705

I think the preprint is still fine. The fundamental sequences in the first definition are of a somewhat preliminary nature. So (\xi:\xi<\beta)$ is the fundamental sequence for $\beta$. The fundamental sequences one is interested in come on page 4.