{"id":"W1968754294","doi":"10.1142/s012905410500342x","title":"A CHARACTERIZATION OF THE ARITHMETICAL HIERARCHY BY LANGUAGE EQUATIONS","year":2005,"lang":"en","type":"article","venue":"International Journal of Foundations of Computer Science","topic":"semigroups and automata theory","field":"Computer Science","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"","keywords":"Peano axioms; Arithmetic function; Concatenation (mathematics); Mathematics; Second-order arithmetic; Expressive power; Hierarchy; Class (philosophy); Analytical hierarchy; Discrete mathematics; Characterization (materials science); Property (philosophy); Axiom; Order (exchange); Algebra over a field; Arithmetic; Pure mathematics; Computer science; Theoretical computer science; Analytic hierarchy process","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007743743,0.0000709874,0.0001232795,0.0003215687,0.00009398692,0.0001691801,0.002946586,0.00002123087,0.00002070356],"category_scores_gemma":[0.0001700274,0.00005195893,0.00009992533,0.0006323509,0.0003916112,0.001569192,0.0003534283,0.0001065839,0.000003728165],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007151508,"about_ca_system_score_gemma":0.0003162503,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005148553,"about_ca_topic_score_gemma":0.000001280071,"domain_scores_codex":[0.9981812,0.00005507829,0.000539877,0.0001325611,0.0009784169,0.0001128377],"domain_scores_gemma":[0.9978631,0.000174455,0.0006097142,0.0003045335,0.0009939553,0.00005423854],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"bench_or_experimental","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000008728871,0.0003830571,0.0003321505,0.000004652294,0.00005301203,0.00000196567,0.002600732,0.00110615,0.4740578,0.2499673,0.0001899704,0.2712944],"study_design_scores_gemma":[0.0009501018,0.0002063887,0.01897749,0.000210769,0.00002187552,0.0002104448,0.000055134,0.6404462,0.3251603,0.00919125,0.004334153,0.0002357939],"study_design_candidate":"bench_or_experimental","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2643176,0.00001882505,0.7306858,0.004077133,0.0007449524,0.0000424924,0.000008468361,0.000007780967,0.00009686379],"genre_scores_gemma":[0.9260548,0.000007150791,0.07348254,0.0002574002,0.0001647863,9.135289e-7,0.000002268186,0.000002645907,0.00002743718],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6617372,"threshold_uncertainty_score":0.5475539,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008621856616376914,"score_gpt":0.2751047152778128,"score_spread":0.2664828586614359,"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."}}