## Sunday, January 5, 2014

### 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.