{"id":"W4287075693","doi":"10.48550/arxiv.2107.07636","title":"An undecidable extension of Morley's theorem on the number of countable models","year":2021,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Austrian Science Fund; Natural Sciences and Engineering Research Council of Canada; Österreichischen Akademie der Wissenschaften","keywords":"Undecidable problem; Countable set; Mathematics; Discrete mathematics; Extension (predicate logic); Continuum hypothesis; Equivalence (formal languages); Decidability; Combinatorics; Computer science","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":[0.004041581,0.0009488984,0.001430413,0.002081695,0.002138041,0.004956068,0.003954053,0.002112346,0.006206172],"category_scores_gemma":[0.02023827,0.0007716233,0.002793401,0.00153626,0.005529139,0.01469481,0.004543495,0.006510472,0.0004910776],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003050866,"about_ca_system_score_gemma":0.00205335,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001551914,"about_ca_topic_score_gemma":0.001821122,"domain_scores_codex":[0.995033,0.0008610474,0.0002698745,0.001514745,0.001732786,0.0005885749],"domain_scores_gemma":[0.9649497,0.02623984,0.001621907,0.004017659,0.002023579,0.001147261],"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":[0.0001139271,0.0001194629,0.002370907,0.0001755427,0.00005339258,0.0002690945,0.000247172,0.01700389,0.002413251,0.9596755,0.003985974,0.01357189],"study_design_scores_gemma":[0.00002720234,0.00002323034,0.0004251949,0.00002098152,0.00002416846,0.0001119005,0.00005544622,0.05894761,0.002206996,0.9359965,0.002138968,0.00002183582],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2870601,0.001056159,0.6616884,0.007136283,0.000478731,0.0001161097,0.001291439,0.0009900801,0.04018275],"genre_scores_gemma":[0.8894947,0.0004859373,0.09930237,0.001161662,0.0006201656,0.0002448896,0.0009789377,0.0002258028,0.007485528],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006206172,"threshold_uncertainty_score":0.02213567,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1473086203965276,"score_gpt":0.2579607926624747,"score_spread":0.1106521722659471,"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."}}