# 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 universality,graphs,prikry forcing,iterated forcing,master conditions,successors of singular cardinals,laver indestructibility Faculty of Science > School of Mathematics Pure Connector 22 Mar 2016 09:05 04 Apr 2021 00:31 https://ueaeprints.uea.ac.uk/id/eprint/57615 10.1017/jsl.2015.65

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