Ramified Forcing, Kartoniert / Broschiert

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 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 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.