### Universal graphs at the successor of a singular cardinal

by Dzamonja and Shelah. [DjSh:659]

J Symbolic Logic, 2003

The paper is concerned with the existence of a universal graph
at the successor of a strong limit singular mu of cofinality
aleph_0 . 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 2^{mu^+}>> 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.

Back to the list of publications