Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata

Details Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata

1999-07-07

arxiv.org/abs/math/9907046v1

Mathematics

Logic

13 pages

Scientific paper

We show that if the weak compactness of a cardinal is made indestructible by
means of any preparatory forcing of a certain general type, including any
forcing naively resembling the Laver preparation, then the cardinal was
originally supercompact. We then apply this theorem to show that the hypothesis
of supercompactness is necessary for certain proof schemata.

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