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Small universal families for graphs omitting cliques without GCH

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Abstract

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 λ+-graphs (λ regular) omitting cliques of some finite or uncountable cardinality, it is consistent that there are small universal families and 2λ > λ+. In particular, we get such a result for triangle-free graphs.

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  1. Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8-10/104, Wien, 1040, Austria

    Katherine Thompson

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  1. Katherine Thompson
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Correspondence to Katherine Thompson.

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Thompson, K. Small universal families for graphs omitting cliques without GCH. Arch. Math. Logic 49, 799–811 (2010). https://doi.org/10.1007/s00153-010-0197-4

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  • DOI: https://doi.org/10.1007/s00153-010-0197-4

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