Authors: Guzmán, Osvaldo
Todorčević, Stevo 
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Forcing with copies of the Rado and Henson graphs
Journal: Annals of Pure and Applied Logic
Volume: 174
Issue: 8
First page: 103286
Issue Date: 2023
Rank: ~M21
ISSN: 0168-0072
DOI: 10.1016/j.apal.2023.103286
If B is a relational structure, define P(B) the partial order of all substructures of B that are isomorphic to it. Improving a result of Kurilić and the second author, we prove that if R is the random graph, then P(R) is forcing equivalent to S⁎R˙, where S is Sacks forcing and R˙ is an ω-distributive forcing that is not forcing equivalent to a σ-closed one. We also prove that P(H3) is forcing equivalent to a σ-closed forcing, where H3 is the generic triangle-free graph.
Keywords: Henson graph | Poset of copies | Random graph | Sacks forcing | Ultrahomogenous graphs
Publisher: Elsevier

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