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arXiv · 1612.01572

Strongly proper forcing and some problems of Foreman

Sean Cox·Monroe Eskew
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Abstract

We provide solutions to several problems of Foreman about ideals, several of which are closely related to Mitchell's notion of \emph{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~\cite{MR2768692} about ideal projections which is more comprehensive and simpler than the solution obtained in \cite{MR3343538}. 2) We solve an older question from Foreman~\cite{MR819932} about the relationship between generic hugeness and generic almost hugeness. 3) Finally, we provide solutions to two technical questions from Foreman~\cite{MR3038554} and \cite{MR2768692} related to his \emph{Duality Theorem}.

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Sean Cox, Monroe Eskew. 2016-12-05. Strongly proper forcing and some problems of Foreman. https://arxiv.org/abs/1612.01572

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