{"paper":{"title":"Copies of the Random Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Milo\\v{s} S. Kurili\\'c, Stevo Todor\\v{c}evi\\'c","submitted_at":"2014-10-23T11:21:29Z","abstract_excerpt":"Let $(R, \\sim )$ be the Rado graph, $Emb (R)$ the monoid of its self-embeddings, $\\Pi (R)=\\{ f[R]: f\\in Emb (R)\\}$ the set of copies of $R$ contained in $R$, and ${\\mathcal I}_R$ the ideal of subsets of $R$ which do not contain a copy of $R$. We consider the poset $( \\Pi (R ), \\subset )$, the algebra $P (R)/{\\mathcal I _R}$, and the inverse of the right Green's pre-order on $Emb (R)$, and show that these pre-orders are forcing equivalent to a two step iteration of the form $P \\ast \\pi$, where the poset $P$ is similar to the Sacks perfect set forcing: adds a generic real, has the $\\aleph _0$-co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6320","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}