Universal graphs at the successor of a singular cardinal

Džamonja, Mirna; Shelah, Saharon

J. Symbolic Logic, Tome 68 (2003) no. 1, p. 366- 388 / Harvested from Project Euclid

Résumé

The paper is concerned with the existence of a universal graph at the successor of a strong limit singular μ of cofinality \aleph₀. Starting from the assumption of the existence of a supercompact cardinal, a model is built in which for some such μ there are μ⁺⁺ graphs on μ⁺ that taken jointly are universal for the graphs on μ⁺, while $2^μ⁺ \gg μ⁺⁺$. 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 κ exists. The result on the existence of universal graphs is obtained as a specific application of a more general method.

Publié le : 2003-06-14
Classification:

@article{1052669056,
     author = {D\v zamonja, Mirna and Shelah, Saharon},
     title = {Universal graphs at the successor of a singular cardinal},
     journal = {J. Symbolic Logic},
     volume = {68},
     number = {1},
     year = {2003},
     pages = { 366- 388},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1052669056}
}

Džamonja, Mirna; Shelah, Saharon. Universal graphs at the successor of a singular cardinal. J. Symbolic Logic, Tome 68 (2003) no. 1, pp.  366- 388. http://gdmltest.u-ga.fr/item/1052669056/