# Sh:659

• Džamonja, M., & Shelah, S. (2003). Universal graphs at the successor of a singular cardinal. J. Symbolic Logic, 68(2), 366–388.
• Abstract:
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.
• Version 2002-11-20_11 (36p) published version (24p)
Bib entry
@article{Sh:659,
author = {D{\v{z}}amonja, Mirna and Shelah, Saharon},
title = {{Universal graphs at the successor of a singular cardinal}},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {68},
number = {2},
year = {2003},
pages = {366--388},
issn = {0022-4812},
mrnumber = {1976583},
mrclass = {03E35 (03E55 03E75)},
doi = {10.2178/jsl/1052669056},
note = {\href{https://arxiv.org/abs/math/0102043}{arXiv: math/0102043}},
arxiv_number = {math/0102043}
}