Forcings which preserve large cardinals
Sy-David Friedman (2010)
Acta Universitatis Carolinae. Mathematica et Physica
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Sy-David Friedman (2010)
Acta Universitatis Carolinae. Mathematica et Physica
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Sy-David Friedman (2009)
Acta Universitatis Carolinae. Mathematica et Physica
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Menachem Magidor (1978)
Fundamenta Mathematicae
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Arthur Apter, James Henle (1991)
Fundamenta Mathematicae
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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.
Julius Barbanel (1991)
Fundamenta Mathematicae
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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.
Arthur Apter (1984)
Fundamenta Mathematicae
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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.
Stanisław Roguski (1990)
Colloquium Mathematicae
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F. Drake (1970)
Fundamenta Mathematicae
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Arthur W. Apter (2015)
Bulletin of the Polish Academy of Sciences. Mathematics
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We construct a model for the level by level equivalence between strong compactness and supercompactness with an arbitrary large cardinal structure in which the least supercompact cardinal κ has its strong compactness indestructible under κ-directed closed forcing. This is in analogy to and generalizes the author's result in Arch. Math. Logic 46 (2007), but without the restriction that no cardinal is supercompact up to an inaccessible cardinal.
Arthur W. Apter (2012)
Bulletin of the Polish Academy of Sciences. Mathematics
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We show that certain relatively consistent structural properties of the class of supercompact cardinals are also relatively consistent with the Wholeness Axioms.