Definition:Proper Relational Structure

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Definition

Let $A$ be a set or class.

Let $\RR$ be a relation on $A$.

Then $\struct {A, \RR}$ is a proper relational structure if and only if:

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

Sources

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