Definition:Primitive Recursive

Function
A function is primitive recursive if it can be obtained from basic primitive recursive functions using the operations of substitution and primitive recursion a finite number of times.

Set
Let $$A \subseteq \N$$.

Then $$A$$ is a primitive recursive set iff its characteristic function $$\chi_A$$ is a primitive recursive function.

Relation
Let $$\mathcal{R} \subseteq \N^k$$ be an $n$-ary relation on $$\N^k$$.

Then $$\mathcal{R}$$ is a primitive recursive relation iff its characteristic function $$\chi_{\mathcal{R}}$$ is a primitive recursive function.