User blog comment:Syst3ms/A sketch for an — actually — formal definition of UNOCF/@comment-35470197-20180803231131/@comment-35392788-20180807064024

@PsiCubed2

No, Username never ever stated that his Mahlos and weakly compacts were as strong as in standard OCFs. I'll ask him on Discord for confirmation, but I think I already know the answer.

And then yes, the C function is just a shorthand and can always be replaced with things like U(M^M^w). But I thought you had figured out that Username is not good at making stuff remotely formalizable, let alone close to standard.

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.