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

James Cummings, Mirna Dzamonja, Charles Morgan

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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.
Original languageEnglish
Pages (from-to)541-569
Number of pages29
JournalJournal of Symbolic Logic
Volume81
Issue number02
Early online date29 Jun 2016
DOIs
Publication statusPublished - Jun 2016

Keywords

  • Universality
  • graphs
  • Prikry forcing
  • iterated forcing
  • master conditions
  • successors of singular cardinals
  • Laver indestructibility

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