# Definition:Proper Relational Structure

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## Definition

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).

## Sources

- 2010: Raymond M. Smullyan and Melvin Fitting:
*Set Theory and the Continuum Problem*(revised ed.): $\S 10.1$