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A lifting argument for generalized Gregorieff forcing

Publication at Faculty of Arts |
2016

Abstract

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-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.