Universal graphs at the successor of a singular cardinal

Journal of Symbolic Logic 68 (2):366-388 (2003)
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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DOI 10.2178/jsl/1052669056
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References found in this work BETA
Simple Unstable Theories.Saharon Shelah - 1980 - Annals of Mathematical Logic 19 (3):177-203.
Toward Classifying Unstable Theories.Saharon Shelah - 1996 - Annals of Pure and Applied Logic 80 (3):229-255.
Adding Closed Cofinal Sequences to Large Cardinals.Lon Berk Radin - 1982 - Annals of Mathematical Logic 22 (3):243-261.
The Universality Spectrum of Stable Unsuperstable Theories.Menachem Kojman & Saharon Shelah - 1992 - Annals of Pure and Applied Logic 58 (1):57-72.

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Models of Real-Valued Measurability.Sakae Fuchino, Noam Greenberg & Saharon Shelah - 2006 - Annals of Pure and Applied Logic 142 (1):380-397.

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