{"id":"W1909164099","doi":"10.1007/978-1-4757-3490-4_1","title":"Axiomatic Systems and Finite Geometries","year":2001,"lang":"en","type":"book-chapter","venue":"Undergraduate texts in mathematics","topic":"History and Theory of Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Euclidean geometry; Axiom; Completeness (order theory); Axiomatic system; Independence (probability theory); Simple (philosophy); Consistency (knowledge bases); Foundations of geometry; Projective test; Mathematics; Algebra over a field; Calculus (dental); Computer science; Pure mathematics; Projective geometry; Geometry; Mathematical analysis; Epistemology; Differential geometry","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.001760259,0.001161157,0.002105002,0.001232081,0.0002462278,0.000200344,0.0006361844,0.0008467219,0.0003531685],"category_scores_gemma":[0.001384148,0.001096269,0.0002755293,0.0002170331,0.000573814,0.0002002648,0.0002764405,0.0009559761,0.0004501269],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003368978,"about_ca_system_score_gemma":0.0001163732,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005792367,"about_ca_topic_score_gemma":0.00004709447,"domain_scores_codex":[0.9954492,0.00008644893,0.00205525,0.0007322123,0.0009750275,0.0007018254],"domain_scores_gemma":[0.9920122,0.004842123,0.001324468,0.001416761,0.0001525006,0.0002519397],"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":[0.00001093794,0.000207197,0.000002391526,0.005863231,0.0002010927,0.0002121223,0.001701282,0.00002594476,0.000003496852,0.9858404,0.005262102,0.000669825],"study_design_scores_gemma":[0.0005862048,0.00009111079,3.603531e-7,0.003804104,0.0003090573,0.0003643514,0.0002590211,0.001677742,0.000004768537,0.9194463,0.07244663,0.001010312],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.0006190481,0.002799083,0.01131119,0.000292757,0.0005946545,0.0017065,0.00007533171,0.0004601022,0.9821413],"genre_scores_gemma":[0.00629823,0.001807477,0.01490447,0.00006761431,0.000224352,0.00007261943,0.00003313215,0.0004932403,0.9760989],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.06718453,"threshold_uncertainty_score":0.9991487,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04872971497162692,"score_gpt":0.2717910975743721,"score_spread":0.2230613826027452,"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."}}