Relational Structures

Overview

A relational structure is a nonempty set $A$ and a collection of relations on $A$. A binary relational structure $⟨A,R⟩$ is a nonempty set $A$ and a binary relation $R$ on $A$.

Isomorphisms

Let $⟨A,R⟩$ and $⟨B,S⟩$ be binary relational structures. An isomorphism from $⟨A,R⟩$ onto $⟨B,S⟩$ is a one-to-one function $f$ from $A$ onto $B$ satisfying:

If such an isomorphism exists, then we say that $⟨A,R⟩$ is isomorphic to $⟨B,S⟩$, denoted $⟨A,R⟩\simeq ⟨B,S⟩$.