User blog comment:Kyodaisuu/Mashimo function/@comment-1605058-20140706065714/@comment-5150073-20140707103956

Peng, I don't know what's the "usual" definition for the "first recursively inaccessible", so I can't claim whether my variant differs from it or not.

Kyodaisuu, if we're only able to compute, say, $$\Sigma(n)$$ and recursive entensions around it, then we can reach only $$f_{\omega_1^\text{CK}+\alpha}(n)$$, where $$\alpha$$ is an ordinal measuring strength of the recursive function. The limit would be thus $$\omega_1^\text{CK}*2$$, not $$\omega_2^\text{CK}$$.