{"id":"W1981966241","doi":"10.1007/s11787-013-0084-y","title":"A Reduction Theorem for the Kripke–Joyal Semantics: Forcing Over an Arbitrary Category can Always be Replaced by Forcing Over a Complete Heyting Algebra","year":2013,"lang":"en","type":"article","venue":"Logica Universalis","topic":"Advanced Algebra and Logic","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Calgary; The King's University; Western University","funders":"University of Calgary","keywords":"Mathematics; Forcing (mathematics); Kripke semantics; Order (exchange); Algebra over a field; Combinatorics; Pure mathematics; Intermediate logic; Mathematical analysis; Description logic","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0003916578,0.0003563365,0.0003454792,0.0001152643,0.0009291789,0.0003261572,0.001128098,0.0001490605,0.0001103696],"category_scores_gemma":[0.00006401156,0.000261976,0.0001912006,0.0003876699,0.0001948571,0.00151519,0.0003162754,0.0003305611,0.000006210063],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001597643,"about_ca_system_score_gemma":0.00006864552,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001254889,"about_ca_topic_score_gemma":0.00008135445,"domain_scores_codex":[0.9975926,0.0001566269,0.0003527105,0.0008357901,0.0003282169,0.00073403],"domain_scores_gemma":[0.9980709,0.0003870217,0.0003120573,0.0009161466,0.0001285821,0.0001852923],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00008277145,0.0001117246,0.0002125733,0.00004539206,0.0001283364,0.00002459558,0.006663002,0.001319765,0.03398707,0.9384847,0.01150387,0.007436226],"study_design_scores_gemma":[0.002789427,0.0009037348,0.001661921,0.00009076006,0.0001460943,0.0001394075,0.008137463,0.5739971,0.004801992,0.3904134,0.01537737,0.001541343],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3152608,0.0003074944,0.6705182,0.00602333,0.0007525004,0.001870273,0.00006574045,0.000812689,0.004389022],"genre_scores_gemma":[0.9812746,0.00003316208,0.01580886,0.001959658,0.0002120231,0.00005779811,0.00006540067,0.00003780696,0.000550711],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6660138,"threshold_uncertainty_score":0.9999833,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02164358199467545,"score_gpt":0.2343952923612789,"score_spread":0.2127517103666034,"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."}}