{"id":"W4293768525","doi":"10.1090/proc/16106","title":"Ramsey theory over partitions III: Strongly Luzin sets and partition relations","year":2022,"lang":"en","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"H2020 European Research Council; Natural Sciences and Engineering Research Council of Canada; Israel Science Foundation","keywords":"Partition (number theory); Mathematics; Ramsey theory; Combinatorics","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":[0.0009938802,0.000403875,0.0004974605,0.0013635,0.001506452,0.003826219,0.0005644226,0.0006317397,0.004433468],"category_scores_gemma":[0.002201584,0.0004362988,0.0007797171,0.001206146,0.004916878,0.004683267,0.001957461,0.002233368,0.0006341104],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002720384,"about_ca_system_score_gemma":0.0006829212,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003068229,"about_ca_topic_score_gemma":0.003257426,"domain_scores_codex":[0.9992866,0.000234597,0.00003095096,0.0001764075,0.0001569116,0.0001146289],"domain_scores_gemma":[0.9989654,0.0005535632,0.00008725103,0.0001599812,0.0001429953,0.00009082107],"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":[0.000008102717,0.0000019525,0.00007272972,0.00001297269,0.000002184632,0.00001292919,0.0001574919,0.0002443627,0.0003031896,0.9972538,0.0005911666,0.001339073],"study_design_scores_gemma":[0.000005256596,0.000008947179,0.0003102347,0.00002532932,0.000008458779,0.00004715022,0.0002044951,0.00197855,0.0006282858,0.9885249,0.008249105,0.000009377688],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.3040535,0.009947943,0.2946754,0.005648225,0.0009660131,0.00004624356,0.0006066791,0.0006628575,0.3833932],"genre_scores_gemma":[0.9526401,0.001242372,0.01875517,0.0006603929,0.0003762238,0.00005119565,0.0002421218,0.0001218562,0.02591054],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004433468,"threshold_uncertainty_score":0.0197379,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01838454958307207,"score_gpt":0.2954668410609177,"score_spread":0.2770822914778456,"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."}}