{"id":"W2032706742","doi":"10.1142/s0219061308000695","title":"GANZSTELLENSÄTZE IN THEORIES OF VALUED FIELDS","year":2008,"lang":"en","type":"article","venue":"Journal of Mathematical Logic","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"Natural Sciences and Engineering Research Council of Canada; Israel Science Foundation","keywords":"Mathematics; Algebraically closed field; Pure mathematics; Valuation ring; Valuation (finance); Algebraic number; Class (philosophy); Model theory; Algebra over a field; Field (mathematics); Ordered field; Point (geometry); Differential (mechanical device); Discrete mathematics; Mathematical analysis; Computer science; Artificial intelligence","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009667469,0.0001184585,0.0005938522,0.0001231141,0.00003799342,0.000002183027,0.0002242732,0.0001506204,0.0005487414],"category_scores_gemma":[0.002638206,0.00007854081,0.0001655245,0.000120992,0.0003227438,0.00009355137,0.00003956123,0.0003546083,0.00001488222],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000197754,"about_ca_system_score_gemma":0.00004414087,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":2.28951e-7,"about_ca_topic_score_gemma":5.412138e-7,"domain_scores_codex":[0.9984927,0.0001675272,0.0008502203,0.00007617607,0.0002359248,0.0001774324],"domain_scores_gemma":[0.9972753,0.001935962,0.0004313948,0.0001883726,0.0001121192,0.00005684837],"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":[0.0001241035,0.0003621382,0.0001955965,0.0001265407,0.00002973174,0.0001833507,0.001769156,0.00002130274,0.0001170769,0.9967456,0.0002302568,0.000095111],"study_design_scores_gemma":[0.0005203325,0.0002390147,0.0001487893,0.0001096319,0.00002424807,0.0006657479,0.0004903257,0.00004840062,0.001371265,0.9962816,0.00002303759,0.00007756409],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8600298,0.0003341001,0.1155405,0.0004525491,0.0001389626,0.0001249457,0.000001411409,0.00001496466,0.0233628],"genre_scores_gemma":[0.9515637,0.00006381499,0.047817,0.00008921264,0.00005519805,0.000001232192,1.058611e-7,0.00001007523,0.0003996419],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.09153394,"threshold_uncertainty_score":0.6008334,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06899874187594827,"score_gpt":0.3360748217710604,"score_spread":0.2670760798951121,"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."}}