{"paper":{"title":"Trace definability I: preservation and characterizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Trace definability is a weakening of definability under which some classification-theoretic properties are preserved and can be characterized.","cross_cats":[],"primary_cat":"math.LO","authors_text":"Erik Walsberg","submitted_at":"2025-04-07T23:47:12Z","abstract_excerpt":"We introduce a notion of weak definability of first order structures, show that various classification-theoretic properties are or are not preserved under it, and that the properties which are preserved can also be characterized in terms of it."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Various classification-theoretic properties are or are not preserved under trace definability, and the properties which are preserved can also be characterized in terms of it.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The introduced notion of trace definability is a coherent and useful weakening of ordinary definability that interacts meaningfully with the classification-theoretic properties under consideration.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Introduces trace definability for first-order structures and establishes preservation and characterization results for classification-theoretic properties under it.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Trace definability is a weakening of definability under which some classification-theoretic properties are preserved and can be characterized.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1260cc163855f118e09b9e03bee6152cb2b548bba762e7636b955e604838759f"},"source":{"id":"2504.05566","kind":"arxiv","version":3},"verdict":{"id":"670f62ed-4986-4f86-befa-5ec25ee8caeb","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-22T21:16:37.689757Z","strongest_claim":"Various classification-theoretic properties are or are not preserved under trace definability, and the properties which are preserved can also be characterized in terms of it.","one_line_summary":"Introduces trace definability for first-order structures and establishes preservation and characterization results for classification-theoretic properties under it.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The introduced notion of trace definability is a coherent and useful weakening of ordinary definability that interacts meaningfully with the classification-theoretic properties under consideration.","pith_extraction_headline":"Trace definability is a weakening of definability under which some classification-theoretic properties are preserved and can be characterized."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.05566/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"ce1e17c02261f5f487fafb81b4ce97e22b7e7162ab92555d44179f07768edef8"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}