# Characterizing forcing extensions

Set theory seminarFriday, November 18, 201610:00 amGC 6417

# Characterizing forcing extensions

I shall present a proof of a theorem of Bukovský from 1973 that characterizes the set-forcing extensions among all pairs of ZFC models $M\subseteq N$: these are precisely the pairs satisfying a uniform covering property. His result has recently resurfaced in the study of set-theoretic geology and can, for example, also be used to give a conceptual proof of (a version of) the intermediate model theorem.