{"id":"W1993827888","doi":"10.1016/j.apal.2005.04.005","title":"Structures interpretable in models of bounded arithmetic","year":2005,"lang":"en","type":"article","venue":"Annals of Pure and Applied Logic","topic":"Computability, Logic, AI Algorithms","field":"Computer Science","cited_by":7,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"Engineering and Physical Sciences Research Council; University of Toronto","keywords":"Pigeonhole principle; Mathematics; Bounded function; Converse; Discrete mathematics; Injective function; Reverse mathematics; Intuitionism; Combinatorics; Mathematical analysis; Axiom","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001627084,0.0009495595,0.001159811,0.002104115,0.00244849,0.007571345,0.001811588,0.00231826,0.007564279],"category_scores_gemma":[0.006666654,0.001229673,0.001820829,0.002280229,0.006186408,0.01390237,0.003220293,0.005700434,0.0008667525],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002681061,"about_ca_system_score_gemma":0.001291889,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002165361,"about_ca_topic_score_gemma":0.00266358,"domain_scores_codex":[0.9982256,0.0006502931,0.0001433212,0.0002784782,0.0004553427,0.0002470504],"domain_scores_gemma":[0.995586,0.00262256,0.0004166429,0.0006849726,0.0004916897,0.0001980167],"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":[0.00001819294,0.000009201525,0.00007158543,0.0000207521,0.000005899646,0.00004149813,0.000245783,0.001021649,0.0002444714,0.9968965,0.0003451026,0.001079485],"study_design_scores_gemma":[0.000007747765,0.000003131336,0.0000266044,0.000007499444,0.000005427906,0.00001457911,0.00004914807,0.002484241,0.0001437647,0.996347,0.0009066604,0.000004163748],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2453651,0.002144336,0.6321393,0.00645435,0.0004733761,0.0001595381,0.001517305,0.001959652,0.109787],"genre_scores_gemma":[0.9279338,0.0006603868,0.05810006,0.0006059537,0.0003012205,0.0001568316,0.001132538,0.000231653,0.01087757],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007571345,"threshold_uncertainty_score":0.02530503,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04767424812238859,"score_gpt":0.2869142189680694,"score_spread":0.2392399708456808,"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."}}