Small universal families of graphs on $\aleph_{\omega+1}$
  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. 
James Cummings, Mirna D\v{z}amonja and Charles Morgan
math.LO