Small universal families for graphs omitting cliques without GCH

When no single universal model for a set of structures exists at a given cardinal, then one may ask in which models of set theory does there exist a small family which embeds the rest. We show that for +-graphs ( regular) omitting cliques of some finite or uncountable cardinality, it is consistent that there are small universal families and 2 > +. In particular, we get such a result for triangle-free graphs.

• Type: Journal
• Year: 2010
• Where: AML
• Authors: Katherine Thompson
• Keywords: AML 2010, Single Universal Model, Small Family, Small Universal Families