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

James Cummings, Mirna Džamonja, Charles Morgan

Published 2014-08-19Version 1

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