Definition:Relational Structure
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Definition
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.
Remarks
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.
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Exercise $14.9$
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.): $\S 10.1$