{"id":"W4388684986","doi":"10.48550/arxiv.2311.06872","title":"Ramsey theorem for trees with successor operation","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Grantová Agentura České Republiky; European Commission; Univerzita Karlova v Praze; National Science Foundation","keywords":"Successor cardinal; Mathematics; Ramsey's theorem; Ramsey theory; Combinatorics; Generalization; Discrete mathematics; Forcing (mathematics); Tree (set theory); Mathematical analysis; Graph","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":[0.001172296,0.0003585913,0.0004773562,0.001100505,0.00110178,0.001215757,0.0006431938,0.0004791817,0.005515197],"category_scores_gemma":[0.002025382,0.0002379432,0.0007170461,0.0006902796,0.002615718,0.004725832,0.00214467,0.001962085,0.0008438738],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008688382,"about_ca_system_score_gemma":0.0005926072,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009507486,"about_ca_topic_score_gemma":0.001081154,"domain_scores_codex":[0.9995658,0.00008262818,0.00002198967,0.0001156648,0.0001292688,0.00008458104],"domain_scores_gemma":[0.998908,0.0005349076,0.00009368079,0.0001505616,0.0001777929,0.0001350009],"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":[0.00000799884,0.000006651178,0.0001139653,0.00003252321,0.000004229556,0.00003464077,0.0001391066,0.0006075768,0.0009575313,0.9927894,0.0009838099,0.00432252],"study_design_scores_gemma":[0.000006766151,0.00001389565,0.0002214738,0.00001420116,0.000009275269,0.0001163686,0.00004595054,0.004782203,0.001019627,0.9830785,0.0106807,0.00001095246],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1659893,0.00387752,0.6619421,0.00398933,0.0005186614,0.00009523159,0.000689787,0.0007296095,0.1621686],"genre_scores_gemma":[0.9042755,0.001754963,0.07005721,0.001101411,0.0005018578,0.0001262517,0.0003092413,0.0001609719,0.02171253],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005515197,"threshold_uncertainty_score":0.01845014,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1590190650424416,"score_gpt":0.2534032070647728,"score_spread":0.09438414202233111,"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."}}