Changing cofinality of cardinals
Menachem Magidor (1978)
Fundamenta Mathematicae
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Displaying similar documents to “Making the hugeness of ϰ resurrectable after ϰ-directed closed forcing”
Changing cofinality of cardinals
An ordering of normal ultrafiltres
Julius Barbanel (1985)
Fundamenta Mathematicae
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Forcing when there are large cardinals: An introduction
Sy-David Friedman (2009)
Acta Universitatis Carolinae. Mathematica et Physica
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Relative consistency results via strong compactness
Arthur Apter, James Henle (1991)
Fundamenta Mathematicae
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Forcings which preserve large cardinals
Sy-David Friedman (2010)
Acta Universitatis Carolinae. Mathematica et Physica
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A generalized version of the singular cardinals problem
Arthur Apter (1984)
Fundamenta Mathematicae
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On weak cardinal powers in generic extensions
F. Drake (1970)
Fundamenta Mathematicae
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On Helling cardinals
A. Wojciechowska (1972)
Fundamenta Mathematicae
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Cardinals and iterations of HOD
Stanisław Roguski (1990)
Colloquium 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.
Indestructible Strong Compactness and Level by Level Equivalence with No Large Cardinal Restrictions
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.
On iterated forcing for successors of regular cardinals
Todd Eisworth (2003)
Fundamenta Mathematicae
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We investigate the problem of when ≤λ-support iterations of < λ-complete notions of forcing preserve λ⁺. We isolate a property- properness over diamonds-that implies λ⁺ is preserved and show that this property is preserved by λ-support iterations. Our condition is a relative of that presented by Rosłanowski and Shelah in [2]; it is not clear if the two conditions are equivalent. We close with an application of our technology by presenting a consistency result on uniformizing colorings...