Definition:Recursively Defined Mapping/Peano Structure

Definition
Let $\left({P, 0, s}\right)$ be a Peano structure.

Let $T$ be a set.

Let $g: T \to T$ be a mapping.

Let $f: P \to T$ be the mapping defined as:


 * $\forall x \in P: f \left({x}\right) = \begin{cases}

a & : x = 0 \\ g \left({f \left({n}\right)}\right) & : x = s \left({n}\right) \end{cases}$

where $a \in T$.

Then $f$ is said to be recursively defined on $P$.

Also see

 * Principle of Recursive Definition/Peano Structure