User blog comment:Tetramur/My thoughts about functions and numbers/@comment-35470197-20191229115044/@comment-35470197-20191229234418

@Plain'N'Simple

> Isn't there a theorem that says that admissible ordinals (those of the form ωαCK) are exactly those who can be "recursively" defined with Oracle TM's?

It is incorrect. Even no oracle Turing machine can compute ω_1^{CK}.

@Tetramur

> Yes, there is such a theorem.

Please tell me the precise statement.

> I'm surprised. You got my idea. Yes, I had in mind some form of "hyper-recursion". I dunno what is it going to be, but it sounds... interesting.

I have already told you about the notion of hypercomputation... Do you start ignoring feedbacks for you?

> It seems to me that we have the same thoughts...

No, you are not even understanding what Plain'N'Simple stated. Honestly, you are not understanding FGH because you believe that FGH is well-defined for uncountable ordinals.