On Grothendieck universes
N. H. Williams (1969)
Compositio Mathematica
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N. H. Williams (1969)
Compositio Mathematica
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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.
G. P. Monro (1974)
Colloquium Mathematicae
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Julius Barbanel (1985)
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.
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.
F. Drake (1970)
Fundamenta Mathematicae
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Josef Šlapal (1993)
Czechoslovak Mathematical Journal
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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.
Arthur Apter, James Henle (1991)
Fundamenta Mathematicae
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