---
tag: A2CE7G6RE6
kind: concept
name: Ramified forcing
sources:
  - wikipedia: en:15634017@r1211749164
    locator: Ramified forcing
    note: adopted
    mention: wikipedia://en/15634017
    sections: [Summary]
same_as:
  wikidata: Q7289554
  wikipedia: Ramified forcing
inventory: [3805B8F1BT]
---

## 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|0MN2MER9WN]] from [[Zermelo–Fraenkel set theory|0HE5WDQ9FJ]]. 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|0QV2JS9RJ3]] to $M$, imitating Kurt Gödel's constructible hierarchy.