Supercompactness and partial level by level equivalence between strong compactness and strongness
Arthur W. Apter
Fundamenta Mathematicae, Tome 184 (2004), p. 123-136 / Harvested from The Polish Digital Mathematics Library
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We force and construct a model containing supercompact cardinals in which, for any measurable cardinal δ and any ordinal α below the least beth fixed point above δ, if δ+α is regular, δ is δ+α strongly compact iff δ is δ + α + 1 strong, except possibly if δ is a limit of cardinals γ which are δ+α strongly compact. The choice of the least beth fixed point above δ as our bound on α is arbitrary, and other bounds are possible.

Publié le : 2004-01-01
EUDML-ID : urn:eudml:doc:283015 
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Arthur W. Apter. Supercompactness and partial level by level equivalence between strong compactness and strongness. Fundamenta Mathematicae, Tome 184 (2004) pp. 123-136. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm182-2-3/