Definition:Relational Structure
Contents
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.
Having gone this far down the road, it is essential now to write a page explaining why it is not actually a mathematical object.
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it. To discuss this point in more detail, feel free to use the talk page.
If you are able to explain it, then when you have done so you can remove this instance of {{Explain}} from the code.
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.): $\S 10.1$
