4.2 Substructures
A structure may contain smaller structures inside it, provided that the smaller domain is closed under the operations of the language and carries the relations inherited from the larger structure. Definition 4.13 (Substructure) Let $\mathcal A$ and $\mathcal B$ be structures for the same signature, and let $A$ and $B$ be their underlying domains. We say that $\mathcal A$ is a substructure of $\mathcal B$, written: $$ \mathcal A \subseteq...