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Universal Indestructibility

Arthur W. Apter·Joel David Hamkins
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Abstract

From a suitable large cardinal hypothesis, we provide a model with a supercompact cardinal in which universal indestructibility holds: every supercompact and partially supercompact cardinal kappa is fully indestructible by kappa-directed closed forcing. Such a state of affairs is impossible with two supercompact cardinals or even with a cardinal which is supercompact beyond a measurable cardinal.

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Arthur W. Apter, Joel David Hamkins. 1998-08-03. Universal Indestructibility. https://arxiv.org/abs/math/9808004

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