Geodesic
Indestructible Strong Compactness and Level by Level Equivalence with No Large Cardinal Restrictions
Arthur W. Apter1
1 Department of Mathematics Baruch College of CUNY New York, NY 10010, U.S.A. and The CUNY Graduate Center, Mathematics 365 Fifth Avenue New York, NY 10016, U.S.A.
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) no. 3, pp. 185-194

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

We construct a model for the level by level equivalence between strong compactness and supercompactness with an arbitrary large cardinal structure in which the least supercompact cardinal $\kappa $ has its strong compactness indestructible under $\kappa $-directed closed forcing. This is in analogy to and generalizes the author’s result in Arch. Math. Logic 46 (2007), but without the restriction that no cardinal is supercompact up to an inaccessible cardinal.
DOI : 10.4064/ba8014-12-2015
Keywords: construct model level level equivalence between strong compactness supercompactness arbitrary large cardinal structure which least supercompact cardinal kappa has its strong compactness indestructible under kappa directed closed forcing analogy generalizes author result arch math logic without restriction cardinal supercompact inaccessible cardinal

Arthur W. Apter 1

1 Department of Mathematics Baruch College of CUNY New York, NY 10010, U.S.A. and The CUNY Graduate Center, Mathematics 365 Fifth Avenue New York, NY 10016, U.S.A. 
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Arthur W. Apter. Indestructible Strong Compactness and Level by Level Equivalence with No Large Cardinal Restrictions. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) no. 3, pp. 185-194. doi: 10.4064/ba8014-12-2015

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