User blog comment:Tetramur/Pentational arrays and beyond - comparisons/@comment-37993808-20191211162933/@comment-35470197-20191212121549

> 1

Wrong Answer. The "order" in that realm is ill-defined because FGH heavily depends on fundamental sequences. Moreover, there is no reasonable known fundamental sequences for ω_1^{CK} such that BB is comparable to f_{ω_1^{CK}}.

> (but ordinal is still computable, because there are only countably many Turing machines).

No. Do you know the definition of computability?

> 2

Wrong Answer. Even second order BB is not comparable to ω_1^CK in any reasonable sense. I am now certain that you do not understand the precise definition of ω_2^{CK}.

> 3

Wrong Answer by the same reason above.

> 4

Wrong answer. The original estimation is not based on actual set theory. It means that you just believed what others said.

> it is still a computable ordinal, as there are only countably many combinators.

No. Do you know the definition of the computability of ordinals?

> 5

Wrong Answer. Your "countable and hence computable" logic make no sense. As I wrote, please honestly write what you actually understand. If you understood the definition of the computability, you would not state such a criterion.

> 6

Wrong Answer. First of all, FOST is just a language.

> So, I think that the ordinal representing Rayo's function in FGH is uncomputable

Is the "compactness" related to the computability? No way. For example, Rayo's number itself is an ordinal, which does not admit a "compact" description in ZFC, while it is a computable ordinal.

> 7

Wrong Answer, because your answer for 6 makes no sense.