A Coloring Theorem for Successors of Singular Cardinals
نویسنده
چکیده
We formulate and prove (in ZFC) a strong coloring theorem which holds at successors of singular cardinals, and use it to answer several questions concerning Shelah’s principle Pr1(μ, μ+, μ+, cf(μ)) for singular μ.
منابع مشابه
Getting more colors II
We formulate and prove (in ZFC) a strong coloring theorem which holds at successors of singular cardinals, and use it to answer several questions concerning Shelah’s principle Pr1(μ, μ+, μ+, cf(μ)) for singular μ.
متن کاملGetting More Colors
We establish a coloring theorem for successors of a singular cardinals, and use it prove that for any such cardinal μ, we have μ+ 9 [μ+]2 μ+ if and only if μ+ 9 [μ]θ for arbitrarily large θ < μ.
متن کاملSuccessors of singular cardinals and coloring theorems {II}
In this paper, we investigate the extent to which techniques used in [8], [2], and [3] — developed to prove coloring theorems at successors of singular cardinals of uncountable cofinality — can be extended to cover the countable cofinality case.
متن کاملGetting more colors I
We establish a coloring theorem for successors of singular cardinals, and use it prove that for any such cardinal μ, we have μ+ 9 [μ+]2 μ+ if and only if μ+ 9 [μ]θ for arbitrarily large θ < μ.
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 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:
دوره شماره
صفحات -
تاریخ انتشار 2009