Abstract
The paper is concerned with the existence of a universal graph at the successor of a strong limit singular μ of co�nality ℵ0. 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 2μ+ ≫ 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 k exists. The result on the existence of universal graphs is obtained as a speci�c application of a more general method.
Original language | English |
---|---|
Pages (from-to) | 366-388 |
Number of pages | 23 |
Journal | Journal of Symbolic Logic |
Volume | 68 |
Issue number | 2 |
DOIs | |
State | Published - Jun 2003 |