Universal graphs at the successor of a singular cardinal

Mirna Džamonja, Saharon Shelah

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

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 languageEnglish
Pages (from-to)366-388
Number of pages23
JournalJournal of Symbolic Logic
Volume68
Issue number2
DOIs
StatePublished - Jun 2003

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