Forum:New idea for Church-Kleene ordinal's fundamental sequence

Here LittlePeng9 said that my definition for natural fundamental sequences isn't the problem for recursive notations. So we get that $$f_\alpha(n)$$ is defined for any recursive $$\alpha$$.

We just define then $$\omega_1^\text{CK}[n]$$ as the largest $$\alpha$$ for which $$f_\alpha(n)$$ is definable by n-state Turing machine. Are there any flaws? Ikosarakt1 (talk ^ contribs) 06:09, May 1, 2014 (UTC)