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June 2003 Universal graphs at the successor of a singular cardinal
Mirna Džamonja, Saharon Shelah
J. Symbolic Logic 68(2): 366-388 (June 2003). DOI: 10.2178/jsl/1052669056

Abstract

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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Mirna Džamonja. Saharon Shelah. "Universal graphs at the successor of a singular cardinal." J. Symbolic Logic 68 (2) 366 - 388, June 2003. https://doi.org/10.2178/jsl/1052669056

Information

Published: June 2003
First available in Project Euclid: 11 May 2003

zbMATH: 1055.03030
MathSciNet: MR1976583
Digital Object Identifier: 10.2178/jsl/1052669056

Rights: Copyright © 2003 Association for Symbolic Logic

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Vol.68 • No. 2 • June 2003
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