Inverse and named fixed values, with ↑↑?

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The inverse of $+$ is $-$, of $\times$ is $/$ and of $\text{^}$ is Log.


Continuing upwards hyperoperationally, what is the inverse of $↑↑$?


Whats more somtimes values that are fixed are given names, some being labels such as:

$2\times = \text{double}\\ \text{^}2 = \text{squared}$

And some that are also other functions, such as:

$\text{^}0.5 = \text{square root}\\\text{^}0.33... = \text{cube root}\\\text{^}-1 = \text{reciprocal}$

What are some for ↑↑?