Ramified forcing
In the mathematical discipline of set theory, ramified forcing is the original form of forcing introduced by Script error: No such module "Footnotes". to prove the independence of the continuum hypothesis from Zermelo–Fraenkel set theory. Ramified forcing starts with a model Template:Mvar of set theory in which the axiom of constructibility, V = LScript error: No such module "Check for unknown parameters"., holds, and then builds up a larger model M[G]Script error: No such module "Check for unknown parameters". of Zermelo–Fraenkel set theory by adding a generic subset Template:Mvar of a partially ordered set to Template:Mvar, imitating Kurt Gödel's constructible hierarchy.
Dana Scott and Robert Solovay realized that the use of constructible sets was an unnecessary complication, and could be replaced by a simpler construction similar to John von Neumann's construction of the universe as a union of sets VαScript error: No such module "Check for unknown parameters". for ordinals αScript error: No such module "Check for unknown parameters".. Their simplification was originally called "unramified forcing" Script error: No such module "Footnotes"., but is now usually just called "forcing". As a result, ramified forcing is only rarely used.
References
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