Definition:Relational Structure

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Definition

A relational structure is an ordered pair $\left ({S, \mathcal R}\right)$, where:

$S$ is a set
$\mathcal R$ is an endorelation on $S$.


Also known as

A relational structure may also be called a relational system.


Remarks

In the context of class-set theory, it is common to abuse notation by writing $\left({C, \mathcal R}\right)$ when $C$ is a class and $\mathcal R$ 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.



Sources