High Quality Content by WIKIPEDIA articles! In mathematics, ramified forcing is the original form of forcing introduced by Cohen (1963). Ramified forcing starts with a model M of V = L, and builds up a larger model M[G] of Zermelo–Fraenkel set theory by adding a generic subset G of a poset to M, by imitating Kurt Godel'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 R( ) for ordinals . (This simplification was originally called "unramified forcing" (Shoenfield 1971), but is now usually just called "forcing".) As a result, ramified forcing is only rarely used.

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