User blog comment:MachineGunSuper/Hypersonic Triangle Notation/@comment-30754445-20181109134629/@comment-30754445-20181117211434

Exactly.

That's why I've said the definition is ambiguous.

Pro tip: If you are not 100% certain about how power towers work, don't use them in your notation. They won't As I've already stated in my previous comment here, it doesn't affect the final strength of your notation in any way. The only that matters is the kind of recursion you're doing.

Case in point:

MGS' notation would have been a perfectly well-defined ω×4-level notation, had he used any well-defined expression as his base level. You could set a//b to simply a^b or a*b or a+b or (a^2+b*3+12) or whatever else suits your fancy, and it will still be an ω×4-level notation.

(that's exactly why ordinals are so useful to measure the growth-rate of functions. Ordinals "count" the number and type of repetitions we're doing, and that's the main factor in determining the strength of your notation. You don't need anything else, in order to know how fast your notation grows)