---
tag: MJF9M19E3E
kind: concept
name: Relational structure
msc: [08A02, 03C07]
specializes: [983GZBQYT4]
sources:
  - url: https://en.wikipedia.org/wiki/Structure_(mathematical_logic)
---

## Summary

A relational structure is a set together with a family of relations on it and no operations.
It is a [[structure|983GZBQYT4]] for a [[signature|WDVVEYD6AT]] that has only relation symbols.
Graphs, partially ordered sets and sets with an equivalence relation are relational structures.
They are the other extreme from [[algebraic structures|QJGPT2W0FT]], which have only operations.

## Explanations

### L1 human

A relational structure is a set where some tuples of elements are marked as related.
A graph is the simplest example: the set is the set of vertices, and two vertices are related when there is an edge between them.
A [[partial order|0QV2JS9RJ3]] such as $\le$ on the integers is another example with one binary relation.
Nothing is computed in a relational structure; one only asks whether given elements are related.