{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003398416,0.0001732686,0.0004565937,0.00001167186,0.0002719696,0.000003347995,0.0005869939,0.00006482019,0.00002267717],"category_scores_gemma":[0.0007894757,0.00007724197,0.0005274529,0.0002461521,0.001825678,0.00005633805,0.0002017838,0.0002167858,0.000002219435],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006499627,"about_ca_system_score_gemma":0.00004534712,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002715606,"about_ca_topic_score_gemma":1.712682e-7,"domain_scores_codex":[0.9988828,0.00001739575,0.0003345943,0.0001951636,0.0003201881,0.0002498443],"domain_scores_gemma":[0.9983218,0.0006458932,0.0005851513,0.0002312804,0.0001694833,0.00004635944],"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":[0.0001860014,0.0006621052,0.0005857905,0.0008716669,0.0002157817,1.596692e-7,0.007258255,0.000006446124,0.004240033,0.9726439,0.01291375,0.0004160775],"study_design_scores_gemma":[0.0004404608,0.0002351137,0.0003129708,0.0002152242,0.00009521053,0.00001595044,0.00314608,0.0006949549,0.01547969,0.9789993,0.0002228842,0.0001422096],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9905515,0.000007751664,0.001823409,0.001792324,0.00004116413,0.0007941471,0.00001673936,0.00004179474,0.004931178],"genre_scores_gemma":[0.9653229,0.00001272702,0.03263734,0.000476517,0.00002507986,0.00004407233,2.33551e-7,0.00002907583,0.001452125],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03081392,"threshold_uncertainty_score":0.6726786,"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."}}