{"id":"W2133334995","doi":"10.1142/s021819670900524x","title":"OMITTING TYPES, BOUNDED WIDTH AND THE ABILITY TO COUNT","year":2009,"lang":"en","type":"article","venue":"International Journal of Algebra and Computation","topic":"Advanced Algebra and Logic","field":"Computer Science","cited_by":20,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University; Concordia University","funders":"Natural Sciences and Engineering Research Council of Canada; Nemzeti Fejlesztési Ügynökség; Fonds Québécois de la Recherche sur la Nature et les Technologies; Hungarian Scientific Research Fund; Centre de Recherches Mathématiques","keywords":"Unary operation; Mathematics; Bounded function; Variety (cybernetics); Type (biology); Discrete mathematics; Affine transformation; Algebra over a field; Combinatorics; Pure mathematics; Mathematical analysis; Statistics","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":[0.004822434,0.0008458328,0.001416981,0.002498671,0.002414481,0.005742444,0.00396377,0.001884684,0.004963465],"category_scores_gemma":[0.02007883,0.001230191,0.002517884,0.002476347,0.009418509,0.02659203,0.009504126,0.004268155,0.0009056022],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001516579,"about_ca_system_score_gemma":0.001265645,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002076938,"about_ca_topic_score_gemma":0.001126079,"domain_scores_codex":[0.9927625,0.001370973,0.001104503,0.001708723,0.001512559,0.001540695],"domain_scores_gemma":[0.970704,0.01437289,0.00273133,0.007743304,0.002481814,0.001966671],"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":[0.000174577,0.00004685775,0.002555418,0.0001041705,0.0000268718,0.000354754,0.001141541,0.003439557,0.001860066,0.9811973,0.000659458,0.008439371],"study_design_scores_gemma":[0.00003216059,0.00006242459,0.0004693678,0.00003038237,0.00003877129,0.0003378718,0.0002388542,0.009128131,0.002400792,0.9845093,0.002719218,0.00003279255],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4592167,0.001249105,0.4926005,0.002716177,0.0001553756,0.0001525469,0.001017713,0.001463751,0.04142809],"genre_scores_gemma":[0.9650016,0.0002619134,0.02795844,0.0003001446,0.0001655752,0.0001297357,0.0005709818,0.000169482,0.005442105],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005742444,"threshold_uncertainty_score":0.02550375,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008600406006068288,"score_gpt":0.2718593373967384,"score_spread":0.2632589313906701,"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."}}