2001/02/06 by Mirna Džamonja, Saharon Shelah, Džamonja, Mirna +1
Mathematics · #03E35 #03E55 #03E75 #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03E35 #msc:03E55 #msc:03E75
paper · pdf · doi:10.48550/arxiv.math/0102043
published as J. Symbolic Logic 68 No. 2 (2003) 366--388
arxiv created 2001/02/06 · arxiv updated 2009/11/30
The paper is concerned with the existence of a universal graph at the successor of a strong limit singular mu of cofinality aleph0. Starting from the assumption of the existence of a supercompact cardinal, a model is built in which for some such mu there are mu++ graphs on mu+ that taken jointly are universal for the graphs on mu+, while 2mu+>> 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 kappa exists. The result on the existence of universal graphs is obtained as a specific application of a more general method.