{"id":"W4313240499","doi":"10.4153/s0008439522000753","title":"Sequential and distributive forcings without choice","year":2022,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Axiom of choice; Mathematics; Axiom; Constructive set theory; Zermelo–Fraenkel set theory; Urelement; Equivalence (formal languages); Distributive property; Countable set; Forcing (mathematics); Mathematical economics; Axiom independence; Consistency (knowledge bases); Discrete mathematics; Pure mathematics; Set (abstract data type); Set theory; Computer science; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0004646401,0.0001639531,0.0002801427,0.000079928,0.0005773384,0.00002113564,0.0001957642,0.00007148328,0.02244489],"category_scores_gemma":[0.0009925725,0.0001633057,0.00005693008,0.00009037701,0.000245953,0.00002511739,0.0001312022,0.0003797002,0.0004352118],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002147917,"about_ca_system_score_gemma":0.0001088862,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000321963,"about_ca_topic_score_gemma":0.0006065496,"domain_scores_codex":[0.998733,0.0001428596,0.0002401899,0.0002652402,0.000161596,0.0004571004],"domain_scores_gemma":[0.9985875,0.0006713144,0.00007127493,0.0002479411,0.00002909954,0.0003929066],"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":[0.00001745696,0.00003598032,0.0002416658,0.00005919618,0.00002559854,0.00006050014,0.0005322764,0.000002253784,0.00002583921,0.9853126,0.013384,0.0003026432],"study_design_scores_gemma":[0.0003521934,0.00005698513,0.00006837563,0.00001438512,0.00004074474,0.0001638893,0.0005897721,0.00009808451,0.00005822707,0.861518,0.1368258,0.000213583],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.868735,0.0002534847,0.02966043,0.01842716,0.0003541746,0.001308222,0.0005781589,0.0002820863,0.08040133],"genre_scores_gemma":[0.9877731,0.000001589072,0.003362307,0.001111251,0.00006743705,0.0001093171,0.00002047015,0.00003543575,0.007519161],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1237946,"threshold_uncertainty_score":0.9784487,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02590794931177459,"score_gpt":0.2887547828404374,"score_spread":0.2628468335286628,"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."}}