On extensions of supercompactness

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Mathematical Logic Quarterly 61 (3):217-223 (2015)
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Abstract

We show that, in terms of both implication and consistency strength, an extendible with a larger strong cardinal is stronger than an enhanced supercompact, which is itself stronger than a hypercompact, which is itself weaker than an extendible. All of these are easily seen to be stronger than a supercompact. We also study Cn‐supercompactness.

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10.1002/malq.201400030

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Citations of this work

On c-extendible cardinals.Konstantinos Tsaprounis - 2018 - Journal of Symbolic Logic 83 (3):1112-1131.

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References found in this work

C(n)-cardinals.Joan Bagaria - 2012 - Archive for Mathematical Logic 51 (3-4):213-240.
Tall cardinals.Joel D. Hamkins - 2009 - Mathematical Logic Quarterly 55 (1):68-86.
Elementary chains and C (n)-cardinals.Konstantinos Tsaprounis - 2014 - Archive for Mathematical Logic 53 (1-2):89-118.
The large cardinals between supercompact and almost-huge.Norman Lewis Perlmutter - 2015 - Archive for Mathematical Logic 54 (3-4):257-289.
Reducing the consistency strength of an indestructibility theorem.Arthur W. Apter - 2008 - Mathematical Logic Quarterly 54 (3):288-293.

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