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About: Sacks property     Goto   Sponge   NotDistinct   Permalink

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In mathematical set theory, the Sacks property holds between two models of Zermelo–Fraenkel set theory if they are not "too dissimilar" in the following sense. For and transitive models of set theory, is said to have the Sacks property over if and only if for every function mapping to such that diverges to infinity, and every function mapping to there is a tree such that for every the level of has cardinality at most and is a branch of . The Sacks property is used to control the value of certain cardinal invariants in forcing arguments. It is named for Gerald Enoch Sacks.