A Lifting Argument for the Generalized Grigorieff Forcing

Radek Honzík, Jonathan Verner
2016 Notre Dame Journal of Formal Logic  
In this short paper, we describe another class of forcing notions which preserve measurability of a large cardinal κ from the optimal hypothesis, while adding new unbounded subsets to κ. In some ways these forcings are closer to the Cohen-type forcings -e.g. we show that they are not minimalhowever, they share some properties with tree-like forcings. We show that they admit fusion-type arguments which allow for a uniform lifting argument.
doi:10.1215/00294527-3459833 fatcat:r7mzaylptngotnlprbe4fa74im