changing terminology (was: overview paper co-author invitation)

[bo198214]

The "super" terminology has always meant: a rank-4 function that is analogous to a rank-3 function.

Or a rank-n+1 function that is analogous to a rank-n function.
Well but for this usage we dont need the super-terminology.
As long as we are inside the operation ladder that starts with addition (or increment) we can always say tetra-exponential, tetra-logarithm (as Tetratophile already suggested), tetra-root. No need for any "super".

The meaning of "super" in this configuration is also quite cumbersome, to determine the meaning of "super-bla" one has to do the following steps:
1. determine the rank of bla
2. determine the type of bla (power,exponential, logarithm)
3. increment the rank, keep the type.

So outside the hierarchy "super" would not make any sense (no rank, no type).
On the other hand a terminology for the inverse Abel function is desperately needed and it has to be applicable to functions outside the hierarchy.
"Inverse Abel function of the exponential" is just not usable compared to "super-exponential".
And "super" in this new context can be defined very precisely for arbitrary functions.
And it matches the expectation, the super-exponential grows much faster than the exponential (while the old "tetra-logarithm" grows much slower than the logarithm, so one would call it rather sub-logarithm. Like Hoohsmand named his operation ultra exponential and infra logarithm, if I remember correctly).

So summarizing "super" is not needed in the default operation ladder, but a term for "inverse Abel function" is desperately needed outside the operation ladder and "super" is intuitively clear for that usage.

I have a feeling that the push for consistent terminology will leave the corpus of writings on this forum in a state of complete inconsistency.

Yes your are right. And I promise you I will never again change the name of the "intuitive iteration", but if a terminology has deficiencies thats just the course of history that it will be replaced especially if it just starts to develop.

I vote for "superlogarithm" or "Abel function of exponential". No "arcsuper".

superlogarithm can be replaced by tetra-logarithm.
"Abel function of exponential" is correct but too long!
Then make a counter suggestion for "Abel function of foo"!