On iterated forcing for successors of regular cardinals
نویسندگان
چکیده
منابع مشابه
On Iterated Forcing for Successors of Regular Cardinals
We investigate the problem of when ≤ λ–support iterations of < λ–complete notions of forcing preserve λ. We isolate a property — properness over diamonds — that implies λ is preserved and show that this property is preserved by λ–support iterations. Our condition is a relative of that presented in [1]; it is not clear if the two conditions are equivalent. We close with an application of our tec...
متن کاملOn successors of Jónsson cardinals
We show that, like singular cardinals, and weakly compact cardinals, Jensen's core model K for measures of order zero 4] calculates correctly the successors of JJ onsson cardinals, assuming O Sword does not exist. Namely, if is a JJ onsson cardinal then + = +K , provided that there is no non-trivial elementary embedding j : K ?! K. There are a number of related results in ZF C concerning P() in...
متن کاملSuccessors of Singular Cardinals and Coloring Theorems
We investigate the existence of strong colorings on successors of singular cardinals. This work continues Section 2 of [1], but now our emphasis is on finding colorings of pairs of ordinals, rather than colorings of finite sets of ordinals.
متن کاملSouslin trees and successors of singular cardinals
The questions concerning existence of Aronszajn and Souslin trees are of the oldest and most dealt-with in modern set theory. There are many results about existence of h+-Aronszajn trees for regular cardinals A. For these cases the answer is quite complete. (See Jech [6] and Kanamory & Magidor [8] for details.) The situation is quite different when A is a singular cardinal. There are very few r...
متن کاملClones on Regular Cardinals
We investigate the structure of the lattice of clones on an infinite set X . We first observe that ultrafilters naturally induce clones; this yields a simple proof of Rosenberg’s theorem: there are 2 λ many maximal (= “precomplete”) clones on a set of size λ. The clones we construct do not contain all unary functions. We then investigate clones that do contain all unary functions. Using a stron...
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/fm179-3-4