Indestructibility, Strong Compactness, and Level by Level Equivalence
نویسنده
چکیده
We show the relative consistency of the existence of two strongly compact cardinals κ1 and κ2 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 κ1. In the model constructed, κ1’s strong compactness is indestructible under arbitrary κ1-directed closed forcing, κ1 is a limit of measurable cardinals, κ2’s strong compactness is indestructible under κ2-directed closed forcing which is also (κ2,∞)-distributive, and κ2 is fully supercompact.
منابع مشابه
A universal indestructibility theorem compatible with level by level equivalence
We prove an indestructibility theorem for degrees of supercompactness that is compatible with level by level equivalence between strong compactness and supercompactness.
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