{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:H4IQSCKWSRT2KECZ4JCBH5UDZH","short_pith_number":"pith:H4IQSCKW","schema_version":"1.0","canonical_sha256":"3f110909569467a51059e24413f683c9ef502519bfda68ced89e6da2e5178f93","source":{"kind":"arxiv","id":"1304.3606","version":1},"attestation_state":"computed","paper":{"title":"On compactness of logics that can express properties of symmetry or connectivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Tapani Hyttinen, Vera Koponen","submitted_at":"2013-04-12T11:25:22Z","abstract_excerpt":"A condition, in two variants, is given such that if a property P satisfies this condition, then every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. The result is used to prove that for a number of natural properties P speaking about automorphism groups or connectivity, every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. We also give an example of a logic that extends first-order logic, has the compactness property and can express the property \"the cardinality of"},"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":"1304.3606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-12T11:25:22Z","cross_cats_sorted":[],"title_canon_sha256":"128e5a05b191a88d4b58d0324d7a5ac8fa727791e2f1bef8c96b400d774002a4","abstract_canon_sha256":"d0f9284d1993f15864bb75e03f3d499bcfcfa5e2b8fbd3aab873facfe4f3e99a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:26.778813Z","signature_b64":"HpSmqOMMn2zzeB4TrOduogYAQPhK+lcOB/H2iGYbFRQla8j8Zfc2R4y1liDaKaiv+pXmzXNx2ScoKyZb7aEUAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f110909569467a51059e24413f683c9ef502519bfda68ced89e6da2e5178f93","last_reissued_at":"2026-05-18T02:25:26.778301Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:26.778301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On compactness of logics that can express properties of symmetry or connectivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Tapani Hyttinen, Vera Koponen","submitted_at":"2013-04-12T11:25:22Z","abstract_excerpt":"A condition, in two variants, is given such that if a property P satisfies this condition, then every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. The result is used to prove that for a number of natural properties P speaking about automorphism groups or connectivity, every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. We also give an example of a logic that extends first-order logic, has the compactness property and can express the property \"the cardinality of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3606","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":"1304.3606","created_at":"2026-05-18T02:25:26.778402+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.3606v1","created_at":"2026-05-18T02:25:26.778402+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3606","created_at":"2026-05-18T02:25:26.778402+00:00"},{"alias_kind":"pith_short_12","alias_value":"H4IQSCKWSRT2","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"H4IQSCKWSRT2KECZ","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"H4IQSCKW","created_at":"2026-05-18T12:27:46.883200+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/H4IQSCKWSRT2KECZ4JCBH5UDZH","json":"https://pith.science/pith/H4IQSCKWSRT2KECZ4JCBH5UDZH.json","graph_json":"https://pith.science/api/pith-number/H4IQSCKWSRT2KECZ4JCBH5UDZH/graph.json","events_json":"https://pith.science/api/pith-number/H4IQSCKWSRT2KECZ4JCBH5UDZH/events.json","paper":"https://pith.science/paper/H4IQSCKW"},"agent_actions":{"view_html":"https://pith.science/pith/H4IQSCKWSRT2KECZ4JCBH5UDZH","download_json":"https://pith.science/pith/H4IQSCKWSRT2KECZ4JCBH5UDZH.json","view_paper":"https://pith.science/paper/H4IQSCKW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.3606&json=true","fetch_graph":"https://pith.science/api/pith-number/H4IQSCKWSRT2KECZ4JCBH5UDZH/graph.json","fetch_events":"https://pith.science/api/pith-number/H4IQSCKWSRT2KECZ4JCBH5UDZH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H4IQSCKWSRT2KECZ4JCBH5UDZH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H4IQSCKWSRT2KECZ4JCBH5UDZH/action/storage_attestation","attest_author":"https://pith.science/pith/H4IQSCKWSRT2KECZ4JCBH5UDZH/action/author_attestation","sign_citation":"https://pith.science/pith/H4IQSCKWSRT2KECZ4JCBH5UDZH/action/citation_signature","submit_replication":"https://pith.science/pith/H4IQSCKWSRT2KECZ4JCBH5UDZH/action/replication_record"}},"created_at":"2026-05-18T02:25:26.778402+00:00","updated_at":"2026-05-18T02:25:26.778402+00:00"}