User blog comment:Kyodaisuu/Mashimo function/@comment-1605058-20140706065714/@comment-24061664-20140706142216

I added linear interpolation in RC.

In Church-Kleene ordinal, fundamental sequence is defined. It is also known that \(\Sigma\) function grows as fast as CK ordinal. Therefore, I thought that I can use the similar definition. But it seems to be not as easy as that. As \(\mathcal{O}(3 \cdot 5^{11}) = \omega^2\), FGH with CK ordinal defined in this way reaches \(\omega^2\) level at \(n=3 \cdot 5^{11}\), while \(\Sigma(3 \cdot 5^{11})\) is much larger than that. It is true that FGH with CK ordinal with this definition grows faster than any recursive ordinal, but to define fundamental sequence which growth as fast as \(\Sigma\) function is another story... I will think about it.