Definition:Age (Model Theory)
Let $\MM$ be an $\LL$-structure.
An age of $\MM$ is a class $K$ of $\LL$-structures such that:
- if $\AA$ is a finitely generated $\LL$-structure such that there is an $\LL$-embedding $\AA \to \MM$, then $\AA$ 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 $\MM$.
That is, $K$ is an age of $\MM$ if it contains exactly one representative from each isomorphism type of the finitely-generated structures that embed into $\MM$.