{"id":"W1987301999","doi":"10.2307/2586526","title":"Pure-projective modules and positive constructibility","year":2000,"lang":"en","type":"article","venue":"Journal of Symbolic Logic","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Manitoba","funders":"","keywords":"Countable set; Mathematics; Converse; Projective cover; Model theory; Pure mathematics; Algebraic number; Discrete mathematics; Quantifier elimination; Projective test; Algebra over a field; Projective space; Collineation; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001199584,0.0004890931,0.000323812,0.001176617,0.0008568892,0.002445007,0.0006662196,0.0005716973,0.004078496],"category_scores_gemma":[0.002173954,0.0003292164,0.0004713547,0.0006644071,0.005960404,0.005370736,0.002550399,0.001384963,0.0003891217],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008059492,"about_ca_system_score_gemma":0.0004435562,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005282059,"about_ca_topic_score_gemma":0.0003929943,"domain_scores_codex":[0.9987369,0.0004938533,0.000047966,0.0001933511,0.0003648259,0.0001630555],"domain_scores_gemma":[0.9983779,0.0006941906,0.0002219612,0.0002351157,0.0002816691,0.0001890855],"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":[0.000005688726,0.00000573014,0.0001824847,0.00001637771,0.000004203883,0.00004476502,0.0002095532,0.0002551319,0.0003372071,0.9971187,0.0002038487,0.001616357],"study_design_scores_gemma":[0.00001051484,0.00002051016,0.0005711578,0.00001272888,0.00001099001,0.0001928205,0.000132284,0.002129379,0.001066406,0.9889286,0.006914712,0.000009856268],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5043499,0.003189923,0.3180091,0.004563211,0.0002130296,0.00006447054,0.0003722236,0.0008975655,0.1683406],"genre_scores_gemma":[0.9849975,0.0004298695,0.00755237,0.0002050406,0.0001415607,0.00003467182,0.00008029,0.0000280849,0.006530518],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004078496,"threshold_uncertainty_score":0.01364398,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02901196460314802,"score_gpt":0.284749259398748,"score_spread":0.2557372947956,"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."}}