User blog comment:Kyodaisuu/Mashimo function/@comment-1605058-20140706065714/@comment-5150073-20140706200402

Peng told me that OTMs are stronger than $$\omega_2^\text{CK}$$. But they're not enough explored to make such claims.

If they can only solve the finite non-computable function and make recursion around it, then they reach only $$\omega_1^\text{CK}$$.

It may also turn that OTM can compute $$\omega_1^\text{CK}[n]$$ and recursion, then they reach $$\omega_2^\text{CK}$$.

If, however, they are able to consider normal "recursive extensions", it will be even larger than $$\omega_{1,2}^\text{CK}$$.