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.

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