User blog comment:Ikosarakt1/Fast-growing hierarchy/@comment-78.22.170.27-20130619192628/@comment-157.193.53.9-20130625141459

Dear all,

as far as I know Gordeev did a closer look at the Taranovsky system some years ago. I will ask him whether he wants to comment further here. From what I read below I conclude that KP+Pi-3 reflection has an ordinal which is smaller than Loader's ordinal. I constructed an embedding of ordinal diagram's into $\psi$-based systems twenty years ago. I also constructed an embedding of Gordeev's notations into the $\psi$-based systems. Things are a bit painful - just remember the Levitz embedding of the ordinal diagrams into the $\theta$-functions in the Intuitionism and Proof Theory proceedings from 68.

Best,

Andreas Weiermann