Forcings which preserve large cardinals
Sy-David Friedman (2010)
Acta Universitatis Carolinae. Mathematica et Physica
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Displaying similar documents to “On iterated forcing for successors of regular cardinals”
Forcings which preserve large cardinals
Forcing when there are large cardinals: An introduction
Sy-David Friedman (2009)
Acta Universitatis Carolinae. Mathematica et Physica
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Changing cofinality of cardinals
Menachem Magidor (1978)
Fundamenta Mathematicae
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Relative consistency results via strong compactness
Arthur Apter, James Henle (1991)
Fundamenta Mathematicae
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Killing GCH everywhere by a cofinality-preserving forcing notion over a model of GCH
Sy-David Friedman, Mohammad Golshani (2013)
Fundamenta Mathematicae
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Starting from large cardinals we construct a pair V₁⊆ V₂ of models of ZFC with the same cardinals and cofinalities such that GCH holds in V₁ and fails everywhere in V₂.
Making the hugeness of ϰ resurrectable after ϰ-directed closed forcing
Julius Barbanel (1991)
Fundamenta Mathematicae
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The consistency of 𝔟 = κ and 𝔰 = κ⁺
Vera Fischer, Juris Steprāns (2008)
Fundamenta Mathematicae
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Using finite support iteration of ccc partial orders we provide a model of 𝔟 = κ < 𝔰 = κ⁺ for κ an arbitrary regular, uncountable cardinal.
A generalized version of the singular cardinals problem
Arthur Apter (1984)
Fundamenta Mathematicae
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Hybrid Prikry forcing
Dima Sinapova (2015)
Fundamenta Mathematicae
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We present a new forcing notion combining diagonal supercompact Prikry forcing with interleaved extender based forcing. We start with a supercompact cardinal κ. In the final model the cofinality of κ is ω, the singular cardinal hypothesis fails at κ, and GCH holds below κ. Moreover we define a scale at κ which has a stationary set of bad points in the ground model.
Cardinals and iterations of HOD
Stanisław Roguski (1990)
Colloquium Mathematicae
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