Small universal families of graphs on $\aleph_{\omega+1}$

Cummings, James, Dzamonja, Mirna and Morgan, Charles (2016) Small universal families of graphs on $\aleph_{\omega+1}$. Journal of Symbolic Logic, 81 (02). pp. 541-569. ISSN 0022-4812

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Abstract

We prove that it is consistent that א_ω is strong limit, 2^{א_ω} is large and the universality number for graphs on א_{ω+1} is small. The proof uses Prikry forcing with interleaved collapsing.

Item Type:	Article
Uncontrolled Keywords:	universality,graphs,prikry forcing,iterated forcing,master conditions,successors of singular cardinals,laver indestructibility
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Logic (former - to 2024) Faculty of Science > Research Groups > Logic (former - to 2024) > Logic (Model Theory, Set Theory) (former - to 2013) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Depositing User:	Pure Connector
Date Deposited:	22 Mar 2016 09:05
Last Modified:	29 Jun 2025 00:18
URI:	https://ueaeprints.uea.ac.uk/id/eprint/57615
DOI:	10.1017/jsl.2015.65

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