THE STRONG TREE PROPERTY AT SUCCESSORS OF SINGULAR CARDINALS
نویسندگان
چکیده
منابع مشابه
The 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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Assuming the existence of a strong cardinal κ and a measurable cardinal above it, we force a generic extension in which κ is a singular strong limit cardinal of any given cofinality, and such that the tree property holds at κ++.
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Strengthening a result of Amir Leshem [7], we prove that the consistency strength of holding GCH together with definable tree property for all successors of regular cardinals is precisely equal to the consistency strength of existence of proper class many Π 1 reflecting cardinals. Moreover it is proved that if κ is a supercompact cardinal and λ > κ is measurable, then there is a generic extensi...
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Starting from the existence of many supercompact cardinals, we construct a model of ZFC + GCH in which the tree property holds at a countable segment of successor of singular cardinals.
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.
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2014
ISSN: 0022-4812,1943-5886
DOI: 10.1017/jsl.2013.3