{"id":"W2095171906","doi":"10.4064/fm168-1-3","title":"Chain conditions in maximal models","year":2001,"lang":"en","type":"article","venue":"Fundamenta Mathematicae","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":33,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Japan Society for the Promotion of Science","keywords":"Mathematics; Counterexample; Axiom; Chain (unit); Axiom of choice; Discrete mathematics; Combinatorics; Mathematical economics; Set theory; Geometry; Computer science; Set (abstract data type)","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":[0.001764227,0.0005123973,0.0007511843,0.001107232,0.002907411,0.002991728,0.001061351,0.00157048,0.0156361],"category_scores_gemma":[0.005302793,0.0005760147,0.001188336,0.0008309002,0.004623951,0.006177962,0.00373896,0.002014691,0.001217591],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002343023,"about_ca_system_score_gemma":0.00120395,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002239842,"about_ca_topic_score_gemma":0.00316639,"domain_scores_codex":[0.9985847,0.0003637643,0.0000723316,0.0003160942,0.0003020118,0.0003609878],"domain_scores_gemma":[0.996668,0.001767321,0.0002554175,0.0004769396,0.0003717021,0.0004606113],"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":[0.00001003442,0.000003395102,0.00006994661,0.000008059704,0.000002018376,0.00002233067,0.00007130692,0.0003701506,0.0001507539,0.9986556,0.0002653551,0.0003709673],"study_design_scores_gemma":[0.00001290849,0.000009208141,0.00006853577,0.00001277302,0.000005725715,0.00002989624,0.00006862276,0.004061534,0.0005837901,0.9933637,0.001776236,0.000007061938],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.3844689,0.001168495,0.2474017,0.004249186,0.0003072472,0.0001216607,0.001155181,0.0009309704,0.3601965],"genre_scores_gemma":[0.9701249,0.0002812785,0.01607637,0.0003209584,0.000094884,0.0001153692,0.0003228865,0.0001093715,0.012554],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0156361,"threshold_uncertainty_score":0.05230802,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08325243727820489,"score_gpt":0.3563066687754133,"score_spread":0.2730542314972084,"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."}}