Universal graphs at the successor of a singular cardinal
Universal graphs at the successor of a singular cardinal
复制标题
单一基数的继任者的通用图
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
S. Shelah
中科院分区：
文献类型：
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作者：
M. Džamonja;S. Shelah
摘要本文讨论了强极限奇异余定μℵ0的后继点上泛图的存在性问题。从超紧基数存在的假设出发，建立了这样一个模型：对于某些这样的μ，μ++上的μ++图的联合取值对μ+上的图是通用的，而.本文还从超紧基数κ存在的假设出发，讨论了在奇异强极限的后继点获得相容结果的框架问题。作为更一般方法的一个具体应用，得到了关于泛图存在性的结果。
Abstract The paper is concerned with the existence of a universal graph at the successor of a strong limit singular μ of cofinality ℵ0. Starting from the assumption of the existence of a supercompact cardinal, a model is built in which for some such μ there are μ++ graphs on μ+ that taken jointly are universal for the graphs on μ+, while . The paper also addresses the general problem of obtaining a framework for consistency results at the successor of a singular strong limit starting from the assumption that a supercompact cardinal κ exists. The result on the existence of universal graphs is obtained as a specific application of a more general method.