{"id":"W2040440669","doi":"10.1016/j.disc.2009.03.018","title":"All countable monoids embed into the monoid of the infinite random graph","year":2009,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":false,"ca_institutions":"Toronto Metropolitan University","funders":"Natural Sciences and Engineering Research Council of Canada; Mitacs","keywords":"Monoid; Mathematics; Countable set; Syntactic monoid; Endomorphism; Free monoid; Combinatorics; Undecidable problem; Discrete mathematics; Graph; Decidability","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009246026,0.0002820424,0.0005181986,0.00005729858,0.0002757843,0.00002789884,0.0007739461,0.0001569686,0.00008264709],"category_scores_gemma":[0.0007208986,0.0001470725,0.0002870543,0.00028373,0.0004279134,0.0001236137,0.0001193473,0.0003558257,0.00001985213],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000272513,"about_ca_system_score_gemma":0.00003705842,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008143787,"about_ca_topic_score_gemma":0.00001688611,"domain_scores_codex":[0.9982501,0.0001849037,0.0006682663,0.0002049341,0.0003439244,0.0003479335],"domain_scores_gemma":[0.997054,0.001212494,0.0004476827,0.001134778,0.00009397216,0.00005704246],"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":[0.000101222,0.0002035132,0.00009311154,0.0001523448,0.0001422031,0.000002591267,0.02117741,0.000162262,0.001394192,0.9746115,0.001485603,0.0004740284],"study_design_scores_gemma":[0.0009277316,0.00005546243,0.00007933091,0.00008324268,0.0001651581,0.00001151745,0.002236974,0.001625699,0.003641817,0.9899431,0.001038783,0.0001911814],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8506223,0.0007001399,0.1050972,0.004109553,0.0004763525,0.001873672,0.0000409382,0.0002488875,0.03683094],"genre_scores_gemma":[0.9753091,0.00009259189,0.0219535,0.0008906742,0.00006864013,0.00003762848,0.000006202132,0.00004158354,0.001600084],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1246868,"threshold_uncertainty_score":0.5997441,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02132264650634368,"score_gpt":0.3049118560055624,"score_spread":0.2835892094992187,"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."}}