Universal graphs at the successor of a singular cardinal

Journal of Symbolic Logic 68 (2):366-388 (2003)
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 $\mu^{++}$ graphs on μ+ that taken jointly are universal for the graphs on μ+, while $2^{\mu^+} \gg \mu^{++}$ . 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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Mirna Džamonja & Saharon Shelah (2004). On -Maximality. Annals of Pure and Applied Logic 125 (1-3):119-158.
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