On extensions of supercompactness
نویسندگان
چکیده
We show that, in terms of both implication and consistency strength, an extendible with a larger strong cardinal is stronger than an enhanced supercompact, which is itself stronger than a hypercompact, which is itself weaker than an extendible. All of these are easily seen to be stronger than a supercompact. We also study C-supercompactness.
منابع مشابه
Consistency Results concerning Supercompactness
A general framework for proving relative consistency results with regard to supercompactness is developed. Within this framework we prove the relative consistency of the assertion that every set is ordinal definable with the statement asserting the existence of a supercompact cardinal. We also generalize Easton's theorem; the new element in our result is that our forcing conditions preserve sup...
متن کاملThe Two-cardinals Transfer Property and Resurrection of Supercompactness
We show that the transfer property (א1,א0)→ (λ+, λ) for singular λ does not imply (even) the existence of a non-reflecting stationary subset of λ+. The result assumes the consistency of ZFC with the existence of infinitely many supercompact cardinals. We employ a technique of “resurrection of supercompactness”. Our forcing extension destroys the supercompactness of some cardinals; to show that ...
متن کاملStationary Reflection and Level by Level Equivalence
We force and construct a model in which level by level equivalence between strong compactness and supercompactness holds, along with certain additional “inner model like” properties. In particular, in this model, the class of Mahlo cardinals reflecting stationary sets is the same as the class of weakly compact cardinals, and every regular Jonsson cardinal is weakly compact. On the other hand, w...
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 کاملA New Easton Theorem for Supercompactness and Level by Level Equivalence ∗†
We establish a new Easton theorem for the least supercompact cardinal κ that is consistent with the level by level equivalence between strong compactness and supercompactness. This theorem is true in any model of ZFC containing at least one supercompact cardinal, regardless if level by level equivalence holds. Unlike previous Easton theorems for supercompactness, there are no limits on the East...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Math. Log. Q.
دوره 61 شماره
صفحات -
تاریخ انتشار 2015