User blog comment:Syst3ms/A sketch for an — actually — formal definition of UNOCF/@comment-35470197-20180803231131/@comment-30754445-20180807144319

You seem to be right about the weakly compacts, but not about Mahlos. At least, not the Mahlos below M(1,0).

So my basic argument is still valid: There's no way to use the C function to create anything between I(1@ω) and M.

So either:

(1) The C function has absolutely no effect on the strength of the system.

-or-

(2) The assumption that UNOCF (when limited up to M) is as strong as Deedlit's OCF (when limited up to M) is wrong.

(and the problem of redundency of the C function just gets worse the farther we progress)

And it seems that we are in agreement on this. You said yourself that option #1 is true.

"As for UNOCF cardinals supposedly catching up to standard, see with Nish. He understands Deedlit's and Rathjen's OCF much better than I could ever hope to do. He's the one who said that psi_T(T^T^T) = Rathjen's K. "

Considering that UNOCF isn't well-defined, and that by that time we reach T it is supposed to work on completely different principles than any previously existing OCF, I doubt there's any meaningful answer to the question "what's the value of  UT(T^T^T). Sure, it can be K if definte it in a certain way. It can also be larger or smaller. At these levels, UNOCF is just a vague idea.

Rreminds me of all the "estimates" for post-tetrational-arrays BEAF we had here, years ago. Since BEAF, at these levels, is nothing more than a rough outline of a notation, different people could easily arrive to different values. Do pentational arrays reach Γ₀ or ζ₀? Niether, because - apparently - there's no way to make pentational arrays work anyway.

(by "work" I mean that they follow Bowers own assumption that {a,b,c} & d has {a,b,c} entries)