Souslin trees at successors of regular cardinals
نویسندگان
چکیده
منابع مشابه
Souslin 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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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...
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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...
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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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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: Mathematical Logic Quarterly
سال: 2019
ISSN: 0942-5616,1521-3870
DOI: 10.1002/malq.201800065