User blog comment:QuasarBooster/Everlasting Egrets/@comment-33713741-20190720113923/@comment-35470197-20190804125227

> There either exists a Turing machine that can simulate any FGH expression with any countable ordinal(s) (in which case any uncomputable function would surpass my function) or there doesn't (in which case I can't create my function)

It depends on what "FGH expression" means. If you allow the FGH along any non-recursive system of fundamental sequences, then it does not necessarily admit a Turing machine simulating it. In this case, there is an uncomputable function which takes values in {0,1}. Therefore if you were correct, your function would take only zero.

If you only allow the FGH along a recursive system of fundamental sequences, then it admits a Turing machine simulating it by definition.