Consistency results concerning supercompactness
نویسندگان
چکیده
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 کاملEaston Functions and Supercompactness
Suppose κ is λ-supercompact witnessed by an elementary embedding j : V →M with critical point κ, and further suppose that F is a function from the class of regular cardinals to the class of cardinals satisfying the requirements of Easton’s theorem: (1) ∀α α < cf(F (α)) and (2) α < β =⇒ F (α) ≤ F (β). In this article we address the question: assuming GCH, what additional assumptions are necessar...
متن کاملSupercompactness and Failures of GCH
Let κ < λ be regular cardinals. We say that an embedding j : V → M with critical point κ is λ-tall if λ < j(κ) and M is closed under κ-sequences in V . Silver showed that GCH can fail at a measurable cardinal κ, starting with κ being κ++-supercompact. Later, Woodin improved this result, starting from the optimal hypothesis of a κ++-tall measurable cardinal κ. Now more generally, suppose that κ ...
متن کاملSome Results concerning Pythagorean Triplets
By using a computer program devised by M. Creutz, we were able to determine all Pythagoeran triplets for which z ^ 300. At this point, a distinction must must be made between P-triplets for which x9 y9 and z have no common divisor [the so-called "primitive solutions" of (1)] and P-triplets which are related to the primitive solutions by multiplication by a common integer factor k. So, if Xi9y^9...
متن کاملMathematical Results concerning Kernel Techniques
that are intended to reproduce observational input/output data pairs (xj ; yj) in the sense F (xj) yj . Such functions have been studied in a general mathematical context for quite some time, and this contribution reviews part of the known facts and provides links to a subset of the background literature. Special emphasis is given to questions of optimality and complexity within the context of ...
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: Transactions of the American Mathematical Society
سال: 1976
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1976-0540771-8