Strongly Proper Forcing and Some Problems of Foreman
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چکیده
We provide solutions to several problems of Foreman about ideals, several of which are closely related to Mitchell’s notion of strongly proper forcing. We prove: (1) Presaturation of a normal ideal implies projective antichain catching, enabling us to provide a solution to a problem from Foreman [8] about ideal projections which is more comprehensive and simpler than the solution obtained in [4]. (2) We solve an older question from Foreman [9] about the relationship between generic hugeness and generic almost hugeness. (3) Finally, we provide solutions to two technical questions from Foreman [7] and [8] related to his Duality Theorem.
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