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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1410.6320","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-10-23T11:21:29Z","cross_cats_sorted":[],"title_canon_sha256":"1e8277fad0ed11f91544bb43bb52dd9bd5af2a389b278470d59e468c3770244e","abstract_canon_sha256":"724293817d32506f551cd8daf6a0a7bc8ca357f72df1a4cd8e5cdf5a358c086c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:32.026489Z","signature_b64":"NbqyYW9vZVS+Sl2b81H4qncRtaT/iYywVz+Jo3zX4IpOiuVpXzqPaK7j9OnC+9xvX1MCxrieB6uAY+Lvr7/5CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"697f19fe32a005b8720791fc8733d3760d0cd7c48a578671ce5ef5dc0fd12e16","last_reissued_at":"2026-05-18T00:34:32.026100Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:32.026100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1410.6320","created_at":"2026-05-18T00:34:32.026153+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.6320v1","created_at":"2026-05-18T00:34:32.026153+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6320","created_at":"2026-05-18T00:34:32.026153+00:00"},{"alias_kind":"pith_short_12","alias_value":"NF7RT7RSUAC3","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"NF7RT7RSUAC3Q4QH","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"NF7RT7RS","created_at":"2026-05-18T12:28:41.024544+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NF7RT7RSUAC3Q4QHSH6IOM6TOY","json":"https://pith.science/pith/NF7RT7RSUAC3Q4QHSH6IOM6TOY.json","graph_json":"https://pith.science/api/pith-number/NF7RT7RSUAC3Q4QHSH6IOM6TOY/graph.json","events_json":"https://pith.science/api/pith-number/NF7RT7RSUAC3Q4QHSH6IOM6TOY/events.json","paper":"https://pith.science/paper/NF7RT7RS"},"agent_actions":{"view_html":"https://pith.science/pith/NF7RT7RSUAC3Q4QHSH6IOM6TOY","download_json":"https://pith.science/pith/NF7RT7RSUAC3Q4QHSH6IOM6TOY.json","view_paper":"https://pith.science/paper/NF7RT7RS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.6320&json=true","fetch_graph":"https://pith.science/api/pith-number/NF7RT7RSUAC3Q4QHSH6IOM6TOY/graph.json","fetch_events":"https://pith.science/api/pith-number/NF7RT7RSUAC3Q4QHSH6IOM6TOY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NF7RT7RSUAC3Q4QHSH6IOM6TOY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NF7RT7RSUAC3Q4QHSH6IOM6TOY/action/storage_attestation","attest_author":"https://pith.science/pith/NF7RT7RSUAC3Q4QHSH6IOM6TOY/action/author_attestation","sign_citation":"https://pith.science/pith/NF7RT7RSUAC3Q4QHSH6IOM6TOY/action/citation_signature","submit_replication":"https://pith.science/pith/NF7RT7RSUAC3Q4QHSH6IOM6TOY/action/replication_record"}},"created_at":"2026-05-18T00:34:32.026153+00:00","updated_at":"2026-05-18T00:34:32.026153+00:00"}