{"id":"W1966303569","doi":"10.1090/s0002-9939-09-10115-6","title":"On the role of the collection principle for Σ⁰₂-formulas in second-order reverse mathematics","year":2009,"lang":"lv","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Computability, Logic, AI Algorithms","field":"Computer Science","cited_by":48,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Banff International Research Station for Mathematical Innovation and Discovery; John Templeton Foundation; National Science Foundation","keywords":"Mathematics; Order (exchange); Reverse mathematics; Calculus (dental); Applied mathematics; Geometry; Axiom","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":[],"consensus_categories":[],"category_scores_codex":[0.002150276,0.0004088341,0.0008732534,0.00004675666,0.0003958524,0.000128748,0.002685001,0.000133574,0.00004290758],"category_scores_gemma":[0.001971361,0.0002168133,0.0009062346,0.002488457,0.001028346,0.0002018296,0.0008641825,0.0005872726,0.000006354892],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003160639,"about_ca_system_score_gemma":0.0001852329,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002507088,"about_ca_topic_score_gemma":0.000004372002,"domain_scores_codex":[0.9967244,0.00005455359,0.001091521,0.0005588547,0.0009543442,0.0006163649],"domain_scores_gemma":[0.9956356,0.001289773,0.001592336,0.0007866282,0.0006061048,0.00008961699],"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":[0.0001033761,0.003928349,0.001392586,0.001579572,0.000240828,1.281682e-7,0.03902246,0.0002718819,0.0103653,0.9308876,0.005395777,0.006812141],"study_design_scores_gemma":[0.0003992864,0.0005014622,0.003326433,0.0003758268,0.00007103959,0.00001043222,0.00371793,0.3388397,0.008541189,0.6436374,0.0003187576,0.0002606552],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.970678,0.00005060977,0.01097333,0.01027169,0.0001751106,0.003431056,0.00002193252,0.00006696708,0.004331301],"genre_scores_gemma":[0.8924415,0.0000162894,0.1055651,0.001190341,0.00007853641,0.00009831005,2.276983e-7,0.00003281007,0.0005769233],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3385678,"threshold_uncertainty_score":0.8841389,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01363867840563703,"score_gpt":0.2547967305169723,"score_spread":0.2411580521113353,"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."}}