Yes, we're back! This is the start of a series where we not only push the numbers bigger, we learn about a new kind of ordinal, and develop a very elegant version of ordinal collapse that makes the fast and slowgrowing hierarchies fit together perfectly. This is all based on an article by S. S. Wainer:
"Slow Growing Versus Fast Growing"
The Journal of Symbolic Logic
Vol. 54, No. 2 (Jun., 1989), pp. 608614