In this short paper, we describe another class of forcing notions which preserve measurability of a large cardinal from the optimal hypothesis, while adding new unbounded subsets to . In some ways these forcings are closer to the Cohen-type forcings—we show that they are not minimal—but, they share some properties with treelike forcings. We show that they admit fusion-type arguments which allow for a uniform lifting argument.
"A Lifting Argument for the Generalized Grigorieff Forcing." Notre Dame J. Formal Logic 57 (2) 221 - 231, 2016. https://doi.org/10.1215/00294527-3459833