{"id":"W1990143438","doi":"10.4064/fm186-1-5","title":"A countable dense homogeneous set of reals of size \\aleph<sub>1</sub>","year":2005,"lang":"en","type":"article","venue":"Fundamenta Mathematicae","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"Natural Sciences and Engineering Research Council of Canada; Consejo Nacional de Ciencia y Tecnología; Grantová Agentura České Republiky","keywords":"Countable set; Aleph; Mathematics; Homogeneous; Set (abstract data type); Discrete mathematics; Pure mathematics; Combinatorics; Computer science","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":[0.0005958882,0.0005341137,0.0006590934,0.001146847,0.001587075,0.002001029,0.0006322382,0.0003046426,0.005643316],"category_scores_gemma":[0.001294282,0.0003989698,0.0008166793,0.0009981428,0.003276528,0.003842719,0.002699109,0.001238936,0.0006350538],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009926169,"about_ca_system_score_gemma":0.0004904255,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001498529,"about_ca_topic_score_gemma":0.001538265,"domain_scores_codex":[0.999411,0.00008201774,0.00002917858,0.000184882,0.0001549005,0.0001380334],"domain_scores_gemma":[0.9984077,0.0006457156,0.0002300305,0.000177641,0.0002506387,0.0002882523],"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":[0.0001080273,0.00002984984,0.0008574083,0.0001126587,0.00002816303,0.0002430607,0.0005554972,0.0006536674,0.01015596,0.9804064,0.001003836,0.005845428],"study_design_scores_gemma":[0.00007158452,0.000231848,0.006200999,0.00005142054,0.0001044593,0.00112309,0.001392374,0.01271523,0.03470391,0.9120611,0.03126689,0.00007707522],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5799347,0.001073332,0.3480541,0.001474569,0.0001395294,0.00007800747,0.001075775,0.000509775,0.06766029],"genre_scores_gemma":[0.9609646,0.0004537463,0.02379333,0.0001789794,0.0001452493,0.00007611357,0.0006100393,0.00004757999,0.01373037],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005643316,"threshold_uncertainty_score":0.01887876,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03719711341625363,"score_gpt":0.3182427990846397,"score_spread":0.2810456856683861,"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."}}