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||Abstract:||
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|
Show full item record
checked on Dec 7, 2023
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.