On the strong equality between supercompactness and strong compactness

Details On the strong equality between supercompactness and strong compactness On the strong equality between supercompactness and strong compactness

1995-02-15

arxiv.org/abs/math/9502232v1

Trans. Amer. Math. Soc. 349(1) (1997), 103-128

Mathematics

Logic

Scientific paper

We show that supercompactness and strong compactness can be equivalent even as properties of pairs of regular cardinals. Specifically, we show that if V models ZFC + GCH is a given model (which in interesting cases contains instances of supercompactness), then there is some cardinal and cofinality preserving generic extension V[G] models ZFC + GCH in which, (a) (preservation) for kappa <= lambda regular, if V models ``kappa is lambda supercompact'', then V[G] models ``kappa is lambda supercompact'' and so that, (b) (equivalence) for kappa <= lambda regular, V[G] models ``kappa is lambda strongly compact'' iff V[G] models ``kappa is lambda supercompact'', except possibly if kappa is a measurable limit of cardinals which are lambda supercompact.

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