# 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. - 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}, doi = {10.2178/jsl/1052669056}, mrclass = {03E35 (03E55 03E75)}, mrnumber = {1976583}, mrreviewer = {P\'eter Komj\'ath}, doi = {10.2178/jsl/1052669056}, note = {\href{https://arxiv.org/abs/math/0102043}{arXiv: math/0102043}}, arxiv_number = {math/0102043} }