Forcing when there are large cardinals: An introduction
Sy-David Friedman (2009)
Acta Universitatis Carolinae. Mathematica et Physica
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Displaying similar documents to “Forcings which preserve large cardinals”
Forcing when there are large cardinals: An introduction
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Killing GCH everywhere by a cofinality-preserving forcing notion over a model of GCH
Sy-David Friedman, Mohammad Golshani (2013)
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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.
On iterated forcing for successors of regular cardinals
Todd Eisworth (2003)
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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...
Hybrid Prikry forcing
Dima Sinapova (2015)
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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.
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.