Definition:Proper Relational Structure
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Definition
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.): $\S 10.1$