In this context, the extension of zeration is addition, which is defined as repeated succession.
The successor function is part of the formal language used to state the Peano axioms, which formalise the structure of the natural numbers.
Several constructions of the natural numbers within set theory have been proposed.
[2] The successor function is the level-0 foundation of the infinite Grzegorczyk hierarchy of hyperoperations, used to build addition, multiplication, exponentiation, tetration, etc.
It was studied in 1986 in an investigation involving generalization of the pattern for hyperoperations.