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2 Bulletin of the Polish Academy of Sciences. Mathematics

2 Apter A. W.

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Indestructible Strong Compactness and Level by Level Equivalence with No Large Cardinal Restrictions

Apter A. W.

Bulletin of the Polish Academy of Sciences. Mathematics

2015

Vol. 63, no. 3

185--194

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 κ has its strong compactness indestructible under κ-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.

Level by Level Inequivalence, Strong Compactness, and GCH

Apter A. W.

Bulletin of the Polish Academy of Sciences. Mathematics

2012

Vol. 60, no 3

201--209

We construct three models containing exactly one supercompact cardinal in which level by level inequivalence between strong compactness and supercompactness holds. In the first two models, below the supercompact cardinal κ, there is a non-supercompact strongly compact cardinal. In the last model, any suitably defined ground model Easton function is realized.