(under construction) Compilation of properties of "tetration"

"Tetration" as "the forth binary arithmetical operation after addition,multiplication,exponentiation" was introduced as iterated exponentiation by ?? Goodstein .

In my view, "iterated exponentiation" means to assume a starting value x_0 , to apply the exponentiation (to some base b) at this x_1 = exp_b(x_0) and do this h-times. In