{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:IRXNOAVIM6JHHDBFXY2WN76EE5","short_pith_number":"pith:IRXNOAVI","schema_version":"1.0","canonical_sha256":"446ed702a86792738c25be3566ffc4275f2aa1ed90ac11c196d1313719bd5c57","source":{"kind":"arxiv","id":"1211.6755","version":3},"attestation_state":"computed","paper":{"title":"Model completeness of o-minimal fields with convex valuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Clifton Ealy, Jana Ma\\v{r}\\'ikov\\'a","submitted_at":"2012-11-28T21:25:46Z","abstract_excerpt":"We let R be an o-minimal expansion of a field, V a convex subring, and $(R_0, V_{0})$ an elementary substructure of (R,V). We let L be the language consisting of a language for R, in which R has elimination of quantifiers, and a predicate for V, and we let $L_{R_{0}}$ be the language L expanded by constants for all elements of $R_0$. Our main result is that (R,V) considered as an $L_{R_{0}}$-structure is model complete provided that $k_R$, the corresponding residue field with structure induced from R, is o-minimal. Along the way we show that o-minimality of $k_R$ implies that the sets definabl"},"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":"1211.6755","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-11-28T21:25:46Z","cross_cats_sorted":[],"title_canon_sha256":"f806a8e16a97c817e09dcc91352695b300a9741b4031e8a77281904198cf8339","abstract_canon_sha256":"726c35b6c8f71aa558104c39cbd3e0aeaffd8e1e9413a06eaf554613d6d61988"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:26.315340Z","signature_b64":"z59Qur3JttYhlJXHc8Y9jk+3vygp4Xkre/SVJcgu3WvotG2F0+UP2LdLMjobuGImRk+kzxTBX7IpVN2hlgwCBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"446ed702a86792738c25be3566ffc4275f2aa1ed90ac11c196d1313719bd5c57","last_reissued_at":"2026-05-18T03:05:26.314795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:26.314795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Model completeness of o-minimal fields with convex valuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Clifton Ealy, Jana Ma\\v{r}\\'ikov\\'a","submitted_at":"2012-11-28T21:25:46Z","abstract_excerpt":"We let R be an o-minimal expansion of a field, V a convex subring, and $(R_0, V_{0})$ an elementary substructure of (R,V). We let L be the language consisting of a language for R, in which R has elimination of quantifiers, and a predicate for V, and we let $L_{R_{0}}$ be the language L expanded by constants for all elements of $R_0$. Our main result is that (R,V) considered as an $L_{R_{0}}$-structure is model complete provided that $k_R$, the corresponding residue field with structure induced from R, is o-minimal. Along the way we show that o-minimality of $k_R$ implies that the sets definabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6755","kind":"arxiv","version":3},"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":"1211.6755","created_at":"2026-05-18T03:05:26.314868+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.6755v3","created_at":"2026-05-18T03:05:26.314868+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6755","created_at":"2026-05-18T03:05:26.314868+00:00"},{"alias_kind":"pith_short_12","alias_value":"IRXNOAVIM6JH","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"IRXNOAVIM6JHHDBF","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"IRXNOAVI","created_at":"2026-05-18T12:27:09.501522+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/IRXNOAVIM6JHHDBFXY2WN76EE5","json":"https://pith.science/pith/IRXNOAVIM6JHHDBFXY2WN76EE5.json","graph_json":"https://pith.science/api/pith-number/IRXNOAVIM6JHHDBFXY2WN76EE5/graph.json","events_json":"https://pith.science/api/pith-number/IRXNOAVIM6JHHDBFXY2WN76EE5/events.json","paper":"https://pith.science/paper/IRXNOAVI"},"agent_actions":{"view_html":"https://pith.science/pith/IRXNOAVIM6JHHDBFXY2WN76EE5","download_json":"https://pith.science/pith/IRXNOAVIM6JHHDBFXY2WN76EE5.json","view_paper":"https://pith.science/paper/IRXNOAVI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.6755&json=true","fetch_graph":"https://pith.science/api/pith-number/IRXNOAVIM6JHHDBFXY2WN76EE5/graph.json","fetch_events":"https://pith.science/api/pith-number/IRXNOAVIM6JHHDBFXY2WN76EE5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IRXNOAVIM6JHHDBFXY2WN76EE5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IRXNOAVIM6JHHDBFXY2WN76EE5/action/storage_attestation","attest_author":"https://pith.science/pith/IRXNOAVIM6JHHDBFXY2WN76EE5/action/author_attestation","sign_citation":"https://pith.science/pith/IRXNOAVIM6JHHDBFXY2WN76EE5/action/citation_signature","submit_replication":"https://pith.science/pith/IRXNOAVIM6JHHDBFXY2WN76EE5/action/replication_record"}},"created_at":"2026-05-18T03:05:26.314868+00:00","updated_at":"2026-05-18T03:05:26.314868+00:00"}