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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Arthur Apter, James Henle (1991)
Fundamenta Mathematicae
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Arthur Apter (1984)
Fundamenta Mathematicae
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Menachem Magidor (1978)
Fundamenta Mathematicae
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A. Wojciechowska (1972)
Fundamenta Mathematicae
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Julius Barbanel (1991)
Fundamenta Mathematicae
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Julius Barbanel (1985)
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.
F. Drake (1970)
Fundamenta Mathematicae
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Arthur W. Apter, Shoshana Friedman (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
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In an attempt to extend the property of being supercompact but not HOD-supercompact to a proper class of indestructibly supercompact cardinals, a theorem is discovered about a proper class of indestructibly supercompact cardinals which reveals a surprising incompatibility. However, it is still possible to force to get a model in which the property of being supercompact but not HOD-supercompact holds for the least supercompact cardinal κ₀, κ₀ is indestructibly supercompact, the strongly...
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.
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.