A Lifting Argument for the Generalized Grigorieff Forcing

Notre Dame Journal of Formal Logic 57 (2):221-231 (2016)
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Abstract

In this short paper, we describe another class of forcing notions which preserve measurability of a large cardinal $\kappa$ from the optimal hypothesis, while adding new unbounded subsets to $\kappa$. 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.

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Citations of this work

A Laver-like indestructibility for hypermeasurable cardinals.Radek Honzik - 2019 - Archive for Mathematical Logic 58 (3-4):275-287.

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References found in this work

The negation of the singular cardinal hypothesis from o(K)=K++.Moti Gitik - 1989 - Annals of Pure and Applied Logic 43 (3):209-234.
Perfect-set forcing for uncountable cardinals.Akihiro Kanamori - 1980 - Annals of Mathematical Logic 19 (1-2):97-114.
The number of normal measures.Sy-David Friedman & Menachem Magidor - 2009 - Journal of Symbolic Logic 74 (3):1069-1080.
Perfect trees and elementary embeddings.Sy-David Friedman & Katherine Thompson - 2008 - Journal of Symbolic Logic 73 (3):906-918.

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