User blog comment:Alemagno12/An extremely fast-growing OCF/@comment-5029411-20170726203426/@comment-30754445-20170727064815

It isn't "ad-hoc" though.

The basic function in Alemagno's notation is "going to the a-th cardinal" which is basically Ωa for any ordinal a. Only this level needs to be "obvious", and it is.

The next levels are supposed to be built in a systemized way on this first one, with the previously created ordinals serving as counters and the L function serving as a "keeper" of the resulting fixed points (which Alemagno calls "omega limits").

This isn't very different, really, from how the ordinary ψ function works. There we have ψ(a)=εa and the "wildcard" symbol of Ω to jump over the fixed points. And this simple system gets us all the way from tame epsilon number to the impressive BHO.

So that's not necessarily a problem.

It all boils down to the question of how powerful the "feedback loop" in the notation is. And we can't really comment on that until he completes his definitions and clean them up so we would have actual examples to work with.