Forcing Fraisse

Maybe it's just because it's three in the morning, but this little throwaway exercise in some lecture notes (pdf) of David Marker made my night:

Two models $\mathcal{M}$ and $\mathcal{N}$ are $\infty$-back-and-forth equivalent iff there is a forcing extension of the universe in which they are isomorphic.

Mind. Blown. And the proof is obvious.