{"id":"W4417424742","doi":"10.1007/s00153-025-01003-1","title":"Limits on forcing axioms at $$\\omega _2$$ compatible with the continuum hypothesis","year":2025,"lang":"en","type":"article","venue":"Archive for Mathematical Logic","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Forcing (mathematics); Axiom; Axiom of choice; Generalization; Limit (mathematics); Zermelo–Fraenkel set theory; Continuum hypothesis; Constructive set theory; Axiom independence","routes":{"ca_aff":true,"ca_fund":true,"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":[0.004688313,0.0007269706,0.001058848,0.002671133,0.004644063,0.005339514,0.0018421,0.002988944,0.01452386],"category_scores_gemma":[0.0123632,0.001114281,0.002533382,0.001402888,0.007362563,0.01554936,0.006419754,0.007777526,0.001723645],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001968731,"about_ca_system_score_gemma":0.001714815,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001107527,"about_ca_topic_score_gemma":0.001438169,"domain_scores_codex":[0.9954469,0.001367618,0.0003519238,0.001031223,0.001080938,0.0007214259],"domain_scores_gemma":[0.9868664,0.007788052,0.0007557482,0.0016668,0.001889143,0.001033904],"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":[0.0000176374,0.00001092446,0.00009821005,0.00001355926,0.000006090634,0.0000694277,0.0001259821,0.0001480621,0.000312618,0.9978577,0.0004487743,0.0008908634],"study_design_scores_gemma":[0.0000114401,0.000007438641,0.0001251358,0.000009647022,0.000005361957,0.00008125347,0.00007247221,0.0007118715,0.0003578535,0.9965911,0.002016869,0.000009481405],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1794872,0.0009797018,0.4664934,0.00882653,0.001436699,0.0001351685,0.001018535,0.0009938944,0.3406288],"genre_scores_gemma":[0.8992696,0.0005365803,0.06385335,0.002151707,0.001084258,0.0003185807,0.0007853308,0.0005060805,0.0314945],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01452386,"threshold_uncertainty_score":0.04858714,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05672658853150693,"score_gpt":0.3179612707031239,"score_spread":0.2612346821716169,"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."}}