The two-cardinals transfer property and resurrection of supercompactness 󠀼span style=󠀢color:red󠀢󠀾This article has been retracted󠀼/span󠀾

Author:

Ben-David Shai,Shelah Saharon

Abstract

We show that the transfer property ( 1 , 0 ) ( λ + , λ ) (\aleph _1,\aleph _0)\to (\lambda ^+,\lambda ) for singular λ \lambda does not imply (even) the existence of a non-reflecting stationary subset of λ + \lambda ^+ . The result assumes the consistency of ZFC with the existence of infinitely many supercompact cardinals. We employ a technique of “resurrection of supercompactness”. Our forcing extension destroys the supercompactness of some cardinals; to show that in the extended model they still carry some of their compactness properties (such as reflection of stationary sets), we show that their supercompactness can be resurrected via a tame forcing extension.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference18 articles.

1. [BD86] S. Ben David, Full reflection of stationary sets, Abstracts Amer. Math. Soc. 7 (1986), 200.

2. Souslin trees and successors of singular cardinals;Ben-David, Shai;Ann. Pure Appl. Logic,1986

3. The weak □* is really weaker than the full □;Ben-David, Shai;J. Symbolic Logic,1986

4. Nonspecial Aronszajn trees on ℵ_{𝜔+1};Ben-David, Shai;Israel J. Math.,1986

5. A Laver-type indestructability for accessible cardinals;Ben-David, Shai,1988

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Successors of Singular Cardinals;Handbook of Set Theory;2009-12-10

2. Canonical structure in the universe of set theory: part two;Annals of Pure and Applied Logic;2006-10

3. SQUARES, SCALES AND STATIONARY REFLECTION;Journal of Mathematical Logic;2001-05

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