{"id":"W2516694310","doi":"10.1016/j.topol.2017.08.021","title":"PFA(S)[S] and countably compact spaces","year":2017,"lang":"en","type":"article","venue":"Topology and its Applications","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Paracompact space; Undecidable problem; Mathematics; Locally compact space; Consistency (knowledge bases); Space (punctuation); Pure mathematics; Countable set; Normal space; Discrete mathematics; Topological space; Hausdorff space; Decidability; Computer science; Topological vector space","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":[0.0001140283,0.00008876987,0.0001609021,0.00002494338,0.001015711,0.00002577095,0.0001407394,0.0001108099,0.0001182478],"category_scores_gemma":[0.0001208847,0.00007795855,0.00001409475,0.00001427309,0.0006245692,0.0001123036,0.00005890668,0.0001232129,0.00003004857],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000005098141,"about_ca_system_score_gemma":0.00001104672,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001149447,"about_ca_topic_score_gemma":0.00003980504,"domain_scores_codex":[0.9995201,0.00002665542,0.00010294,0.000177105,0.00002905764,0.0001442082],"domain_scores_gemma":[0.9991755,0.0003011996,0.0001063448,0.0003308194,0.00002766045,0.00005843958],"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":[0.00001007171,0.00002631062,0.001138674,0.00001512497,0.00001689843,8.809802e-7,0.0001643796,1.311e-7,0.0002549128,0.9966465,0.0005228168,0.001203245],"study_design_scores_gemma":[0.0002753247,0.00002942176,0.006961053,0.000004765118,0.00003490458,0.00005298014,0.000242807,0.00003801466,0.000498477,0.9468955,0.0448556,0.0001111213],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8670588,0.003049504,0.01405405,0.01638352,0.0001602368,0.0008487184,0.00006985022,0.0001793762,0.09819598],"genre_scores_gemma":[0.995522,0.0003378197,0.0008951984,0.0001929521,0.00007035171,0.00003911321,0.000003382961,0.000007816099,0.00293138],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1284632,"threshold_uncertainty_score":0.7812134,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04939739411770473,"score_gpt":0.3771237830996475,"score_spread":0.3277263889819428,"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."}}