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  1. (1 other version)Effective forcing versus proper forcing.Gerald E. Sacks - 1996 - Annals of Pure and Applied Logic 81 (1-3):171-185.
    , a notion of forcing over E, the E-closure of L, is said to be effective if every sideways -generic extension preserves E-closure. There are set notions of forcing in E that do not preserve E-closure. The main theorem below asserts that is effective if and only if it is locally proper, a weak variant of Shelah's notion of proper.
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