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Universal graphs at the successor of a singular cardinal
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- Journal:
- The Journal of Symbolic Logic / Volume 68 / Issue 2 / June 2003
- Published online by Cambridge University Press:
- 12 March 2014, pp. 366-388
- Print publication:
- June 2003
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- Article
- Export citation
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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.
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