An ordering of normal ultrafiltres
Julius Barbanel (1985)
Fundamenta Mathematicae
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Julius Barbanel (1985)
Fundamenta Mathematicae
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A. Wojciechowska (1972)
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 Apter, James Henle (1991)
Fundamenta 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 Apter (1984)
Fundamenta Mathematicae
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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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F. Drake (1970)
Fundamenta Mathematicae
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Aleksandar Jovanović (1977)
Zbornik Radova
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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.
F. Drake (1974)
Fundamenta Mathematicae
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Menachem Magidor (1978)
Fundamenta Mathematicae
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