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 $\mathcal{M}$.