Journal of Symbolic Logic

Universal graphs at the successor of a singular cardinal

Mirna Džamonja and Saharon Shelah

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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 \aleph0. 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 $2μ+ \gg μ++$. 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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J. Symbolic Logic, Volume 68, Issue 2 (2003), 366- 388.

First available in Project Euclid: 11 May 2003

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Džamonja, Mirna; Shelah, Saharon. Universal graphs at the successor of a singular cardinal. J. Symbolic Logic 68 (2003), no. 2, 366-- 388. doi:10.2178/jsl/1052669056.

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