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

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.
Keywords Grigorieff forcing   lifting argument   preserving measurability
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DOI 10.1215/00294527-3459833
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References found in this work BETA

The Negation of the Singular Cardinal Hypothesis From o=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.
Perfect Trees and Elementary Embeddings.Sy-David Friedman & Katherine Thompson - 2008 - Journal of Symbolic Logic 73 (3):906-918.
Fusion and Large Cardinal Preservation.Sy-David Friedman, Radek Honzik & Lyubomyr Zdomskyy - 2013 - Annals of Pure and Applied Logic 164 (12):1247-1273.

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Citations of this work BETA

A Laver-Like Indestructibility for Hypermeasurable Cardinals.Radek Honzik - 2019 - Archive for Mathematical Logic 58 (3-4):275-287.

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