Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 1

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: supercompact

Sortuj według:

Ogranicz wyniki do:

A note on indestructibility and strong compactness

Apter A. W.

Bulletin of the Polish Academy of Sciences. Mathematics

2008

Vol. 56, no 3-4

191-197

If κ < λ are such that κ is both supercompact and indestructible under κ-directed closed forcing which is also (κ+, ∞)-distributive and λ is 2λ supercompact, then by a result of Apter and Hamkins [J. Symbolic Logic 67 (2002)], {δ < κ | δ is δ+ strongly compact yet δ is not δ+ supercompact} must be unbounded in κ. We show that the large cardinal hypothesis on λ is necessary by constructing a model containing a supercompact cardinal κ in which no cardinal δ > κ is 2δ = δ+ supercompact, κ's supercompactness is indestructible under κ-directed closed forcing which is also (κ+, ∞)-distributive, and for every measurable cardinal δ, δ is δ+ strongly compact if δ is δ+ supercompact.