{"id":"W1831390059","doi":"10.1016/j.aim.2018.03.012","title":"Scott ranks of models of a theory","year":2018,"lang":"en","type":"preprint","venue":"Advances in Mathematics","topic":"Computability, Logic, AI Algorithms","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Countable set; Mathematics; Combinatorics; Omega; Bounded function; Rank (graph theory); Isomorphism (crystallography); Model theory; Discrete mathematics; Measure (data warehouse); Spectrum (functional analysis); Set theory; Set (abstract data type); Philosophy; Physics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.001756466,0.0003116877,0.0009180199,0.0002406106,0.00002100512,0.00002992554,0.002774453,0.0002217144,0.00002107867],"category_scores_gemma":[0.000344862,0.0002787051,0.0001908752,0.000365494,0.000413986,0.0004027739,0.003015448,0.0003891528,0.000005461161],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006585965,"about_ca_system_score_gemma":0.0001555844,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006096694,"about_ca_topic_score_gemma":0.000008141801,"domain_scores_codex":[0.9972774,0.000175721,0.001117414,0.000583256,0.0005636257,0.0002825687],"domain_scores_gemma":[0.9955924,0.001070757,0.0008899279,0.002089061,0.0003095529,0.00004828208],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001471193,0.0008995137,0.0001196781,0.005200802,0.00005261958,0.000007029229,0.01035143,0.1164051,0.00003721313,0.8074669,0.00001855374,0.05942652],"study_design_scores_gemma":[0.0001203648,0.00004095011,0.00001732307,0.0004823313,0.000008724187,0.00000312711,0.0000460086,0.3797438,0.0005588623,0.6188107,0.00001885982,0.0001488811],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.009313795,0.003350308,0.9774033,0.00002466235,0.0007296851,0.000529803,0.00001500536,0.00007800646,0.008555427],"genre_scores_gemma":[0.1916095,0.0004968971,0.8077325,0.00001364727,0.00005245455,0.00003327466,0.000001780537,0.00001922615,0.00004068],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.2633387,"threshold_uncertainty_score":0.9999665,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02706178459283569,"score_gpt":0.2989693452877062,"score_spread":0.2719075606948705,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}