User blog comment:Ikosarakt1/Fast-growing hierarchy/@comment-157.193.53.9-20130620120154

Dear all,

the fundamental sequences for the $\psi$-functions are discussed in the book "Proof theory of Impredicative subsystems of analysis" by Buchholz and Schütte. They are also used in:

MR1365142 (97b:03057) Weiermann, Andreas Investigations on slow versus fast growing: how to majorize slow growing functions nontrivially by fast growing ones. Arch. Math. Logic 34 (1995), no. 5, 313–330.

I got moreover private handwritten notes from Buchholz regarding the higher $theta$-functions. These are not published but as usual the notes by Buchholz are very useful.

Regarding higher notation systems it is best to contact Michael Rathjen. He is one of the greatest masters in the field. A useful link might be:

http://miami.uni-muenster.de/servlets/DerivateServlet/Derivate-5965/diss_stegert.pdf

Best,

Andreas Weiermann