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Universal graphs at the successor of a singular cardinal

Published online by Cambridge University Press:  12 March 2014

Mirna Džamonja
School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK, E-mail:, URL:
Saharon Shelah
Institute of Mathematics, Hebrew University of Jerusalem, 91904 Givat Ram, Israel Rutgers University, New Brunswick, NJ, USA, E-mail:, URL:


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.

Research Article
Copyright © Association for Symbolic Logic 2003

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