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.