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A characterization of lifting generics for Sacks-like forcings. (English) Zbl 1236.03035
Summary: The article gives a uniform characterization of generics that are used in the context of liftings of elementary embeddings for the generalized Sacks forcing, and variations thereof. It applies to the majority of arguments using such forcings providing that the trees are required to be singular-splitting, i.e., no splitting at regular levels. The use of singular-splitting trees eliminates the necessity to choose a generic branch from the “tuning fork” object defined in [S.-D. Friedman and K. Thompson, J. Symb. Log. 73, No. 3, 906–918 (2008; Zbl 1160.03035)].
MSC:
03E35 Consistency and independence results
03E55 Large cardinals
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