User blog comment:P進大好きbot/List of common mistakes on formal logic appearing in googology/@comment-30279966-20190928143127/@comment-35470197-20191006062953

The fastest-growing function in articles in this wiki is Fish number 7 as far as I know. If you do not allow it because it is an extension of other functions, then the alternative fast-growing function is Rayo's function.

I note that they use an unspecified second order set theory. If you do not allow an unspecified theory or you restrict the regulation to uncomputable functions in ZFC set theory, then |the ITTM busy beaver function can be a candidate of the fastest-growing function in articles in this wiki.

Also, there are several uncomputable functions which are not published but are defined in blog posts. For example, my function in ZFC set theory surpasses the ITTM busy beaver function, and my function in an extension of MK set theory surpasses a formalisation of Rayo's function by encoding the truth predicate into the satisfaction definable in MK set theory. I do not know other examples of well-defined non-salad considerably large uncomputable large numbers in blog posts. (Many of them are ill-defined or naive extensions.)

In addition, LittlePeng defined the largest number in a consistent extension of Robinson arithmetic. Although it is not given by a function and the extension is not consistent with ZFC set theory, it is considerable as I explained above. It is theoretically impossible to argue the fastest unless we fix a valid theory. Actually, LittlePeng's example is critical at this point. Therefore we need to specify axioms when we consider what is the fastest.