Geodesic
On level by level equivalence and inequivalence between strong compactness and supercompactness
Arthur W. Apter1
1 Department of Mathematics Baruch College of CUNY New York, NY 10010, U.S.A.
Fundamenta Mathematicae, Tome 171 (2002) no. 1, pp. 77-92.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove two theorems, one concerning level by level inequivalence between strong compactness and supercompactness, and one concerning level by level equivalence between strong compactness and supercompactness. We first show that in a universe containing a supercompact cardinal but of restricted size, it is possible to control precisely the difference between the degree of strong compactness and supercompactness that any measurable cardinal exhibits. We then show that in an unrestricted size universe containing many supercompact cardinals, it is possible to have significant failures of GCH along with level by level equivalence between strong compactness and supercompactness, except possibly at inaccessible levels.
DOI : 10.4064/fm171-1-5
Keywords: prove theorems concerning level level inequivalence between strong compactness supercompactness concerning level level equivalence between strong compactness supercompactness first universe containing supercompact cardinal restricted size possible control precisely difference between degree strong compactness supercompactness measurable cardinal exhibits unrestricted size universe containing many supercompact cardinals possible have significant failures gch along level level equivalence between strong compactness supercompactness except possibly inaccessible levels

Arthur W. Apter 1

1 Department of Mathematics Baruch College of CUNY New York, NY 10010, U.S.A. 
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Arthur W. Apter. On level by level equivalence and inequivalence between
strong compactness and supercompactness. Fundamenta Mathematicae, Tome 171 (2002) no. 1, pp. 77-92. doi : 10.4064/fm171-1-5. http://geodesic.mathdoc.fr/articles/10.4064/fm171-1-5/

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