Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

Streszczenie

We show the relative consistency of the existence of two strongly compact cardinals $\kappa _1$ and $\kappa _2$ which exhibit indestructibility properties for their strong compactness, together with level by level equivalence between strong compactness and supercompactness holding at all measurable cardinals except for $\kappa _1$. In the model constructed, $\kappa _1$'s strong compactness is indestructible under arbitrary $\kappa _1$-directed closed forcing, $\kappa _1$ is a limit of measurable cardinals, $\kappa _2$'s strong compactness is indestructible under $\kappa _2$-directed closed forcing which is also $(\kappa _2, \infty )$-distributive, and $\kappa _2$ is fully supercompact.