User blog comment:Tetramur/My thoughts about functions and numbers/@comment-35470197-20191229115044/@comment-37993808-20191230085919

This is a precise statement:

"By a theorem of Sacks, the countable admissible ordinals are exactly those constructed in a manner similar to the Church-Kleene ordinal, but for Turing machines with oracles."

It is not clear for me how it is connected, but this is a result of Sacks, not me.

> hypercomputation

Yes, I have read what it is. It refers to models of computation that can provide outputs that are not Turing-computable. For example, machine that could resolve a halting problem or Entscheidungsproblem would be a hypercomputer. But Rayo's function is also uncomputable and (presumably) grows much more faster than ITTMs and OTMs.

So, I want to divide all uncomputable functions on two classes:

1) Functions which have a connection with Turing machines of some kind (weakly uncomputable),

2) Functions which have a connection with set theory of any order (strongly uncomputable).