User blog comment:Ikosarakt1/Fast-growing hierarchy/@comment-78.22.170.27-20130619192628

Dear everybody,

maybe the following info is of some interest here. Wilfried Buchholz has a preprint available via his homepage regarding fundamental sequences for the Howard ordinal based on the $\theta$ function. This preprint contains complete information how the sequences are defined and why they are converging as expected. His fundamental sequences satisfy the Bachmann property so that it fits nicely for subrecursive hierarchies like the fast and slow growing one. He also has a preprint about for fundamental sequences for $\theta$-based systems for $ID_\nu$. Fundamental sequences for the $\psi$-based systems can be found in the book by Buchholz and Schütte.

Best,

Andreas Weiermann