Ramified forcing

Summary

In the mathematical discipline of set theory, ramified forcing is the original form of forcing introduced by (Cohen 1963) to prove the independence of the continuum hypothesis from Zermelo–Fraenkel set theory. Ramified forcing starts with a model $M$ of set theory in which the axiom of constructibility, $V = L$, holds, and then builds up a larger model $M[G]$ of Zermelo–Fraenkel set theory by adding a generic subset $G$ of a partially ordered set to $M$, imitating Kurt Gödel's constructible hierarchy.