User blog comment:Tetramur/Pentational arrays and beyond - comparisons/@comment-37993808-20191211162933/@comment-37993808-20191212093937

I actually divide the uncomputable functions into two parts:

1. Weakly uncomputable functions - which are obtained if a countable nonrecursive ordinal is used in mapping "ordinals to functions", as in FGH, Hardy's hierarchy, SGH and so on. For example, Busy Beaver functions (with oracles too), xi function, doodle function, Fish fourth function and so on.

2. Strongly uncomputable functions - which are obtained if a uncountable ordinal is used in mapping "ordinals to functions". For example, Rayo's function and Fish seventh function.

I think that some extension of BEAF can be weakly uncomputable, but not strongly uncomputable. Turing machines and cellular automata can be applied to the idea of BEAF more easily that the idea of microlanguage, I think.