Notre Dame Journal of Formal Logic

A Lifting Argument for the Generalized Grigorieff Forcing

Radek Honzík and Jonathan Verner

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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.

Article information

Notre Dame J. Formal Logic Volume 57, Number 2 (2016), 221-231.

Received: 11 April 2013
Accepted: 26 November 2013
First available in Project Euclid: 7 January 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E35: Consistency and independence results 03E55: Large cardinals

Grigorieff forcing lifting argument preserving measurability


Honzík, Radek; Verner, Jonathan. A Lifting Argument for the Generalized Grigorieff Forcing. Notre Dame J. Formal Logic 57 (2016), no. 2, 221--231. doi:10.1215/00294527-3459833.

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