Indestructibility, strongness, and level by level equivalence
نویسندگان
چکیده
منابع مشابه
Indestructibility, Strong Compactness, and Level by Level Equivalence
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-dir...
متن کاملIndestructibility under adding Cohen subsets and level by level equivalence
We construct a model for the level by level equivalence between strong compactness and supercompactness in which the least supercompact cardinal κ has its strong compactness indestructible under adding arbitrarily many Cohen subsets. There are no restrictions on the large cardinal structure of our model.
متن کاملHod-supercompactness, Indestructibility, and Level by Level Equivalence
In an attempt to extend the property of being supercompact but not hod-supercompact to a proper class of indestructibly supercompact cardinals, a theorem is discovered about a proper class of indestructibly supercompact cardinals which reveals a surprising incompatibility. However, it is still possible to force to get a model in which the property of being supercompact but not hod-supercompact ...
متن کاملA 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.
متن کاملIndestructibility, instances of strong compactness, and level by level inequivalence
Suppose λ > κ is measurable. We show that if κ is either indestructibly supercompact or indestructibly strong, then A = {δ < κ | δ is measurable, yet δ is neither δ+ strongly compact nor a limit of measurable cardinals} must be unbounded in κ. The large cardinal hypothesis on λ is necessary, as we further demonstrate by constructing via forcing two models in which A = ∅. The first of these cont...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2003
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm177-1-3