User blog comment:Syst3ms/A sketch for an — actually — formal definition of UNOCF/@comment-35470197-20180803231131/@comment-35392788-20180804124835

The C function is a function made to enumerate cardinals that diagonalize over smaller ones. So, for example :

C(1,0) = I, it diagonalizes over all C(x)

C(1,1) = I_2, it diagonalizes over all C(x) for x > I

C(2,0) diagonalizes over all C(1,x)

C(1,0,0) diagonalizes over all C(x,0)

C(1,0,1) diagonalizes over all C(x,y) for any y > C(1,0,0), the actual value of y doesn't matter.

C(1,1,0) diagonalizes over all C(1,0,x)

C(1;0) = M, it diagonalizes over all C(a,b,...,n)

C(1;1) = M_2, it diagonalizes over all C(a,b,...,n) for n > M

C(2;0) diagonalizes over all C(1;;a,b,...,n)

I know this is kind of all over the place, but I hope you get the intent of the C function so that it be possible to formalize it.