User blog comment:MachineGunSuper/The Hierarchy Replacement Function/@comment-32783837-20171223145318/@comment-32783837-20171224155910

That's actually a better idea, come to think of it.

My thoughts were:

ω↑↑(ω+1)

= ω↑(ω↑↑ω)

ω[n] = n

ω↑(ω↑↑n)

= ω↑↑n+1

but that's terrible, since any further operations on the second  ω will do the same thing.