  A separable Banach space $X$ is said to be finitely determined if for each
separable space $Y$ such that $X$ is finitely representable (f.r.) in $Y$ and
$Y$ is f.r. in $X$ then $Y$ is isometric to $X$. We provide a direct proof
(without model theory) of the fact that every finitely determined space $X$
(isometrically) contains every (separable) space $Y$ which is finitely
representable in $X$. We also point out how a similar argument proves the
Krivine-Maurey theorem on stable Banach spaces, and give the model theoretic
interpretations of some results.
