Definition:Age (Model Theory)

Definition
Let $\mathcal M$ be an $\mathcal L$-structure.

An age of $\mathcal M$ is a class $K$ of $\mathcal L$-structures such that:
 * if $\mathcal A$ is a finitely generated $\mathcal L$-structure such that there is an $\mathcal L$-embedding $\mathcal A \to \mathcal M$, then $\mathcal A$ is isomorphic to some structure in $K$,
 * no two structures in $K$ are isomorphic, and
 * $K$ does not contain any structures which are not finitely generated or do not embed into $\mathcal M$.

That is, $K$ is an age of $\mathcal M$ if it contains exactly one representative from each isomorphism type of the finitely-generated structures that embed into $\mathcal M$.