{"id":"W2022730753","doi":"10.1090/s0002-9939-08-08918-1","title":"On a fragment of the universal Baire property for Σ¹₂ sets","year":2008,"lang":"en","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Baire measure; Omega; Sigma; Baire space; Baire category theorem; Equivalence (formal languages); Pure mathematics; Combinatorics; Discrete mathematics; Physics","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":[0.001860533,0.0009056295,0.001225379,0.002198869,0.002951708,0.003991438,0.001480195,0.001497877,0.01958614],"category_scores_gemma":[0.005736531,0.000875613,0.003090685,0.002305471,0.004990519,0.01527623,0.004658728,0.004484151,0.003564668],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002715627,"about_ca_system_score_gemma":0.0008268385,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.006500138,"about_ca_topic_score_gemma":0.00568616,"domain_scores_codex":[0.9972951,0.0003433157,0.0001901351,0.0008899081,0.0009462774,0.000335341],"domain_scores_gemma":[0.9969446,0.001430798,0.000165522,0.0006275498,0.0006590063,0.0001725012],"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":[0.00002342885,0.000009746549,0.0001104801,0.00004941857,0.000008987611,0.00008599737,0.0002848647,0.0002885933,0.0006453181,0.9893577,0.002125761,0.007009783],"study_design_scores_gemma":[0.00001172476,0.00002644347,0.0003693939,0.00002747917,0.00001757463,0.0002030037,0.0001153246,0.002172227,0.001100552,0.9790571,0.01687595,0.000023184],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.06113,0.002211682,0.6372176,0.003913875,0.0007891284,0.0001358072,0.001600186,0.002152159,0.2908496],"genre_scores_gemma":[0.7253941,0.002149268,0.1699094,0.003789094,0.001263341,0.0003289639,0.004099736,0.001906549,0.09115967],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01958614,"threshold_uncertainty_score":0.06552219,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02722574452182584,"score_gpt":0.2840727604013193,"score_spread":0.2568470158794934,"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."}}