User blog comment:PsiCubed2/How to make Deedlit's Mahlo-level notation more intuitive/@comment-35470197-20180807000338/@comment-35470197-20180809111138

> I think we can safely assume that this is not due to some oversight on his part. The differences are too great.

Exactly. It is so great that it might be reasonable to guess that the origin of Deedlit's OCF is not Rathjen's OCF. If so, this is just a problem on the lack of my knowledge.

And also, this is one of reasons why I am trying to list up references on OCFs with large cardinals. I could not understand why Deedlit did not refer to the original paper by Rathjen in his blog post. (Is it just a local traditional custom in this wiki not to skip references of the original papers?)

> It is also clear that Rathjen's notation is much more complicated and more difficult to understand. So obviously, Deedlit tried to "re-notate it" in a way that's easier to follow.

I agree that the definition of Deedlit's OCF is much easier to understand, although its strength is much more difficult to understand. Namely, isn't it difficult to understand how Deedlit collapsed higher weakly inaccessible cardinals, especially when we consider psi_{chi(a,0)}(b)?

On the other hand, what Rathjen wanted to do is much easier to understand, because he explicitly gave a way to reduce the degree of the weak inaccessibility by using kappa^-, in the same way as Buchholz reduced the cofinality.

Yeah, I know that this is just my subjective thoughts. It might be simply because I first learned OCFs by papers by Buchholz and Rathjen.

> So the first clue I'll investigate, is the PTO of KPM. We know how Rathjen notates it, and we know how Deedlit notates it.

Another problem is, as I wrote in my blog post on references, that Rathjen had not fully proved the equality, if I am correct. He verified half inequality, and just wrote that the opposite half follows from his non-open unpublished preprint.

Rathjen might like such a technique. I remember that he proved that his OCF with Mahlo is definable under ZFC, and stated that the proof of the well-foundedness would appear later in his up-coming preprint. But it has not come even now, if I am correct.

At least, assuming his result, it is good to compare their OCFs as you say. But if Deedlit is active in this wiki, I believe that he will soon tell us the proof. (As I said, I have already asked him.) Maybe it is better for us, because such a comparison with no hint from the creator is very difficult in general.