# Definition:Proper Relational Structure

## Definition

Let $A$ be a set or class.

Let $\mathcal R$ be a relation on $A$.

Then $(A, \mathcal R)$ is a proper relational structure if and only if:

For each $a \in A$, the preimage $\mathcal R^{-1} \left({a}\right)$ of $a$ under $\mathcal R$ is a set (or small class).