Definition:Recursive

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

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

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

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

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