Sh:659

• Džamonja, M., & Shelah, S. (2003). Universal graphs at the successor of a singular cardinal. J. Symbolic Logic, 68(2), 366–388. arXiv: math/0102043 DOI: 10.2178/jsl/1052669056 MR: 1976583
• 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)

@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}
}