An ordering of normal ultrafiltres
Julius Barbanel (1985)
Fundamenta Mathematicae
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Julius Barbanel (1985)
Fundamenta Mathematicae
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Arthur Apter, James Henle (1991)
Fundamenta Mathematicae
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Arthur Apter (1984)
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.
W. Hanf (1964)
Fundamenta Mathematicae
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F. Drake (1970)
Fundamenta Mathematicae
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Aleksandar Jovanović (1980)
Publications de l'Institut Mathématique
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D. W. H. Gillam (1978)
Colloquium Mathematicae
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Arthur W. Apter (2013)
Bulletin of the Polish Academy of Sciences. Mathematics
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We investigate two global GCH patterns which are consistent with the existence of a tall cardinal, and also present some related open questions.
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...
Sy-David Friedman (2009)
Acta Universitatis Carolinae. Mathematica et Physica
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Arthur W. Apter, Grigor Sargsyan (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
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We show how to reduce the assumptions in consistency strength used to prove several theorems on universal indestructibility.
G. P. Monro (1974)
Colloquium 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.
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.