Definition:Relational Structure

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A relational structure is an ordered pair $\struct {S, \RR}$, where:

$S$ is a set
$\RR$ is an endorelation on $S$.

Also known as

A relational structure may also be called a relational system.


In the context of class-set theory, it is common to abuse notation by writing $\struct {C, \RR}$ when $C$ is a class and $\RR$ is a relation on $C$, and to call this a relational structure.

One must take care, as such a relational structure is not actually an ordered pair, or even, in most theories, a mathematical object of any kind, but only notational shorthand for a concept.