User blog comment:P進大好きbot/New Googological Ruler/@comment-39541634-20190722124029/@comment-39541634-20190723113004

> I personally experienced many times that when they talk about Rathjen's OCF, then it was supposed to behave something like UNOCF...

Most of the people here (me included) have never even seen Rathjen's paper. We just accepted Deedlit's statement that his notation is equivalent in strength. Apparently this trust was unfounded.

In fairness, though, a simplifed OCF can often be equivalent to the original. Madore's Extended Psi is far easier to understand than Buchhollz original notation, yet the two notations have the same strength. And once I created, as an exercise for myself, an OCF that reaches the Omega Fixed Point, which is simpler than Deedlit's yet seems to be equivalent in strength.

You just need to be careful when you simplify, not to throw away the wrong stuff :-)

Anyway, I know that you've always had objections to the claimed strength of Deedlit's Mahlo level notation. What amazed me is that this disperancy already starts at ψ(ψI(0)). Rathjen's ψ(ψI(0)) seems to be something like half-a-dozen conceptual leaps bigger than Deedlit's ψ(ψI(0)). It's staggering.

(though in hindsight, I shouldn't really be surprised. It's not the first time the people here, including myself, accepted on consensus "facts" that were later turned out to be wrong. See the BMS fiasco, for example. This is precisely why I've maintained that we don't have any Level 23 googologists here)