mekso ternary operator: Knuth up-arrow notation: a \uparrow \dots \uparrow b of order/with c-2 arrows ("\uparrow") initially, evaluated from right to left; the cth hyperoperator on a by b.

c must be a nonnegative integer. c=0 is the lowest-order hyperoperator in the structure. Thus, for integers: c=0 is succession of/on b (in which case a can be omitted or be any number), c=1 is addition, c=2 is multiplication, c=3 is exponentiation, c=4 is tetration, etc. Notice that right-grouping is in effect for all c; thus x*(y*z) is calculated, rather than (x*y)*z. See also: de'au'u, fe'au'u.

- de'au'u
*(exp!)* - mekso ternary operator: positive super-logarithm; the super-logarithm (inverse operator of hyper-operator with respect to "height" of power tower) of a with base b and of order c-2.
- fe'au'u
*(exp!)* - mekso ternary operator: positive super-root; the bth super-root (inverse operator of hyper-operator with respect to base) of a of order c-2.