Successors of singular cardinals and measurability
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 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 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 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 کاملThe tree property at successors of singular cardinals
Assuming some large cardinals, a model of ZFC is obtained in which אω+1 carries no Aronszajn trees. It is also shown that if λ is a singular limit of strongly compact cardinals, then λ carries no Aronszajn trees.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1985
ISSN: 0001-8708
DOI: 10.1016/0001-8708(85)90092-1