Strongly proper forcing and some problems of Foreman
Logic
2018-03-13 v2
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}.
Keywords
Cite
@article{arxiv.1612.01572,
title = {Strongly proper forcing and some problems of Foreman},
author = {Sean Cox and Monroe Eskew},
journal= {arXiv preprint arXiv:1612.01572},
year = {2018}
}