User blog comment:Syst3ms/A sketch for an — actually — formal definition of UNOCF/@comment-35470197-20180803231131/@comment-25601061-20180807190148

hey i think it's time for me to join the discussion

the C function is actually not necessary and is only used for shorthanding, but it (1) helps to simplify things a lot, especially in analyses, and (2) helps to explain UNOCF, as, for example, we can think of C(1;0;0) in ψC(1;0;0) as corresponding to a comma in C(_;0).

it has some flaws though, such as only being able to express ordinals of the form ψA(x) for some A and x < AA ω, but me and ecl1psed276 have made an extension of UNOCF in which we can have an ordinal V1+x inside of a function Ψ instead of {x} in C and that not only fixes the flaws that C has but can also go beyond by introducing E = V(1,0) to diagonalize over Vx and higher ordinals to go beyond

also @Syst3ms i only said how UNOCF could look like if it was defined as an ordinal notation instead of an OCF, not that I was going to make such a definition (although I could try to do that)