  Based on a construction method introduced by J. Bourgain and F. Delbaen, we
give a general definition of a Bourgain-Delbaen space and prove that every
infinite dimensional separable $\mathcal{L}_\infty$-space is isomorphic to such
a space. Furthermore, we provide an example of a $\mathcal{L}_\infty$ and
asymptotic $c_0$ space not containing $c_0$.
