The tree property at successors of singular cardinals
نویسندگان
چکیده
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.
منابع مشابه
The Tree Property on a Countable Segment of Successors of Singular Cardinals
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.
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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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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++.
متن کاملAronszajn trees and the successors of a singular cardinal
From large cardinals we obtain the consistency of the existence of a singular cardinal κ of cofinality ω at which the Singular Cardinals Hypothesis fails, there is a bad scale at κ and κ++ has the tree property. In particular this model has no special κ+-trees.
متن کاملReview on Todd Eisworth’s Chapter for the Handbook of Set Theory: “successors of Singular Cardinals”
This chapter offers a comprehensive and lucid exposition of the questions and techniques involved in the study of combinatorics of successors of singular cardinals. What is so special about successors of singular cardinals? They are successor cardinals, but are also similar to inaccessible cardinals, in the sense that there is no maximal regular cardinal below them, meaning for instance that th...
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ورودعنوان ژورنال:
- Arch. Math. Log.
دوره 35 شماره
صفحات -
تاریخ انتشار 1996