On Helling cardinals
A. Wojciechowska (1972)
Fundamenta Mathematicae
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A. Wojciechowska (1972)
Fundamenta Mathematicae
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W. Hanf (1964)
Fundamenta Mathematicae
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Aleksandar Jovanović (1980)
Publications de l'Institut Mathématique
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Stanisław Roguski (1990)
Colloquium Mathematicae
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Arthur Apter (1984)
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.
Arthur Apter, James Henle (1991)
Fundamenta Mathematicae
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Arthur W. Apter (2012)
Bulletin of the Polish Academy of Sciences. Mathematics
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We construct three models containing exactly one supercompact cardinal in which level by level inequivalence between strong compactness and supercompactness holds. In the first two models, below the supercompact cardinal κ, there is a non-supercompact strongly compact cardinal. In the last model, any suitably defined ground model Easton function is realized.
Sy-David Friedman (2009)
Acta Universitatis Carolinae. Mathematica et Physica
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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.
Julius Barbanel (1985)
Fundamenta Mathematicae
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Arthur W. Apter (2012)
Fundamenta Mathematicae
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We apply techniques due to Sargsyan to reduce the consistency strength of the assumptions used to establish an indestructibility theorem for supercompactness. We then show how these and additional techniques due to Sargsyan may be employed to establish an equiconsistency for a related indestructibility theorem for strongness.
Arthur W. Apter (2012)
Colloquium Mathematicae
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We establish two new Easton theorems for the least supercompact cardinal that are consistent with the level by level equivalence between strong compactness and supercompactness. These theorems generalize Theorem 1 in our earlier paper [Math. Logic Quart. 51 (2005)]. In both our ground model and the model witnessing the conclusions of our present theorems, there are no restrictions on the structure of the class of supercompact cardinals.