User blog comment:Deedlit11/The slow-growing hierarchy and other hierarchies/@comment-78.22.170.27-20130619191359

Dear everybody,

I devoted indeed some time into the comparison of the slow and fast growing hierarchies and I am willing to share what I know about it with interested people. The latest result which I obtained (jointly with Buchholz) is that the slow and fast growing hierarchy can catch up naturally at $\omega^2$ when one uses fundamental sequences for tree ordinals as in Buchholz's Lecture Notes in Mathematics 897 contribution. One can also arrange (with modified fundamental sequences) for a match up of the slow and fast growing hierarchy at $\Gamma_0$. The major open problem is in my point of view to find the second subrecursively inaccessible ordinal for the standard Buchholz $\psi$-based notations (with standard fundamental sequences). My conjecture is that it will be $\psi_0{\Omega_\Omega_\omega}$. I was able to show that this ordinal is a lower bound.

Best,

Andreas Weiermann