{"id":"W2919009353","doi":"10.1002/malq.201900058","title":"On universal modules with pure embeddings","year":2020,"lang":"en","type":"preprint","venue":"Mathematical logic quarterly","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Manitoba","funders":"","keywords":"Cofinality; Mathematics; Embedding; Lambda; Cardinality (data modeling); Injective function; Abelian group; Countable set; Limit (mathematics); Model theory; Pure mathematics; Discrete mathematics; Combinatorics; Uncountable set; Physics; Computer science; 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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0003424481,0.0009007581,0.001392764,0.0001646808,0.0001486221,0.0002906937,0.0009549977,0.0005964913,0.0008913926],"category_scores_gemma":[0.0003150853,0.0006490828,0.0003878289,0.0001682666,0.0002855675,0.0001134649,0.0002298301,0.001466931,0.0009156611],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001447445,"about_ca_system_score_gemma":0.00009395992,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006618925,"about_ca_topic_score_gemma":0.000006448588,"domain_scores_codex":[0.9963153,0.0001451233,0.0007718795,0.00116559,0.0009214262,0.0006806538],"domain_scores_gemma":[0.9969273,0.0008503546,0.0004819747,0.001232446,0.0001291749,0.0003787356],"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":[0.0001100148,0.0004945492,0.000003497551,0.001766525,0.0002110628,0.0002483377,0.003784755,0.00002529932,0.00005019145,0.9866124,0.005402984,0.001290345],"study_design_scores_gemma":[0.0006016368,0.001351078,0.00002716538,0.001069483,0.0002306638,0.00004438363,0.001034254,0.002990315,0.00009226339,0.9916235,0.0001296119,0.0008057051],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6385562,0.00006968354,0.2686627,0.006241535,0.0004761584,0.002382939,0.0001463727,0.001823814,0.08164056],"genre_scores_gemma":[0.925405,0.000004948691,0.07213638,0.0005367979,0.0004264273,0.0001161022,0.00004634173,0.0001885995,0.001139422],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2868487,"threshold_uncertainty_score":0.9998623,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03884149798080114,"score_gpt":0.2749829034115511,"score_spread":0.2361414054307499,"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."}}