{"id":"W141387592","doi":"10.1007/978-94-007-2582-9_9","title":"The Axiom of Choice in an Elementary Theory of Operations and Sets","year":2012,"lang":"en","type":"book-chapter","venue":"˜The œWestern Ontario series in philosophy of science","topic":"Logic, Reasoning, and Knowledge","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Western University","funders":"","keywords":"Axiom; Axiom of choice; Constructive set theory; Zermelo–Fraenkel set theory; Ethos; Set theory; Mathematics; Urelement; Relation (database); Function (biology); Set (abstract data type); Mathematical economics; Choice function; Discrete mathematics; Algebra over a field; Pure mathematics; Computer science; Philosophy; Data mining","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":[0.001650797,0.0005482867,0.0007155498,0.001187779,0.002396154,0.004500296,0.00156452,0.001731385,0.007489944],"category_scores_gemma":[0.002282703,0.0007210954,0.0008890404,0.001762139,0.01522881,0.008245748,0.001512442,0.004523532,0.001446492],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.005000889,"about_ca_system_score_gemma":0.003932541,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.01585415,"about_ca_topic_score_gemma":0.02176374,"domain_scores_codex":[0.9990006,0.0002665963,0.00006300881,0.0001636856,0.0004108577,0.00009531547],"domain_scores_gemma":[0.9990895,0.0005295692,0.0000277838,0.0001607332,0.0001530687,0.00003944086],"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":[0.000001930838,0.000001049208,0.000007769421,0.00000794342,7.039316e-7,0.000003514479,0.00009526782,0.00004288029,0.00002508713,0.9969779,0.001393395,0.00144251],"study_design_scores_gemma":[0.000003601783,0.000002147712,0.00004425048,0.00001588561,0.000002004734,0.00001281258,0.00002675989,0.0002055423,0.00006066508,0.9625714,0.03705132,0.000003429783],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.009168974,0.0150148,0.2131645,0.01049698,0.001363693,0.00008100601,0.000472478,0.000199246,0.7500383],"genre_scores_gemma":[0.5341979,0.01604111,0.1764748,0.003661557,0.002362739,0.0004965881,0.0007455398,0.0003851833,0.2656346],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01585415,"threshold_uncertainty_score":0.03628415,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03171846241398109,"score_gpt":0.2575778716925028,"score_spread":0.2258594092785217,"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."}}