Successors of singular cardinals and coloring theorems I
نویسندگان
چکیده
منابع مشابه
Successors 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 کاملSuccessors of singular cardinals and coloring theorems I
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 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 کاملA Coloring Theorem for Successors of Singular Cardinals
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 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...
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ژورنال
عنوان ژورنال: Archive for Mathematical Logic
سال: 2005
ISSN: 0933-5846,1432-0665
DOI: 10.1007/s00153-004-0258-7