Continuum Problem at Measurable Cardinals

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 Helling cardinals

A. Wojciechowska (1972)

Fundamenta Mathematicae

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Some applications of Sargsyan's equiconsistency method

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.

Forcings which preserve large cardinals

Sy-David Friedman (2010)

Acta Universitatis Carolinae. Mathematica et Physica

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A Reduction in Consistency Strength for Universal Indestructibility

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.

An ordering of normal ultrafiltres

Julius Barbanel (1985)

Fundamenta Mathematicae

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