{"id":"https://openalex.org/W1985231476","doi":"https://doi.org/10.2307/2586705","title":"Ordinal diagrams for \u03a0<sub>3</sub>-reflection","display_name":"Ordinal diagrams for \u03a0<sub>3</sub>-reflection","publication_year":2000,"publication_date":"2000-09-01","ids":{"openalex":"https://openalex.org/W1985231476","doi":"https://doi.org/10.2307/2586705","mag":"1985231476"},"language":"en","primary_location":{"id":"doi:10.2307/2586705","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586705","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110301130","display_name":"Toshiyasu Arai","orcid":null},"institutions":[{"id":"https://openalex.org/I113306721","display_name":"Hiroshima University","ror":"https://ror.org/03t78wx29","country_code":"JP","type":"education","lineage":["https://openalex.org/I113306721"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Toshiyasu Arai","raw_affiliation_strings":["Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima, 739-8521, Japan E-mail:","Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima, 739-8521, Japan E-mail: arai@mis.hiroshima-u.ac.jp"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima, 739-8521, Japan E-mail:","institution_ids":["https://openalex.org/I113306721"]},{"raw_affiliation_string":"Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima, 739-8521, Japan E-mail: arai@mis.hiroshima-u.ac.jp","institution_ids":["https://openalex.org/I113306721"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110301130"],"corresponding_institution_ids":["https://openalex.org/I113306721"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.12027774,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"65","issue":"3","first_page":"1375","last_page":"1394"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9753999710083008,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9753999710083008,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9746999740600586,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9685999751091003,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.8650270104408264},{"id":"https://openalex.org/keywords/reflection","display_name":"Reflection (computer programming)","score":0.7991061210632324},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.6739857196807861},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.49052923917770386},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4762159287929535},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.4692623019218445},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4460521340370178},{"id":"https://openalex.org/keywords/reflection-principle","display_name":"Reflection principle (Wiener process)","score":0.4369211792945862},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3881300687789917},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38318049907684326},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3753851056098938},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3266732096672058},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.17723217606544495},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.11840584874153137},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07085379958152771}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.8650270104408264},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.7991061210632324},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.6739857196807861},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.49052923917770386},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4762159287929535},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.4692623019218445},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4460521340370178},{"id":"https://openalex.org/C118368358","wikidata":"https://www.wikidata.org/wiki/Q7307248","display_name":"Reflection principle (Wiener process)","level":5,"score":0.4369211792945862},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3881300687789917},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38318049907684326},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3753851056098938},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3266732096672058},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.17723217606544495},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.11840584874153137},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07085379958152771},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C101615488","wikidata":"https://www.wikidata.org/wiki/Q1503307","display_name":"Geometric Brownian motion","level":4,"score":0.0},{"id":"https://openalex.org/C3017618536","wikidata":"https://www.wikidata.org/wiki/Q304994","display_name":"Innovation diffusion","level":2,"score":0.0},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.0},{"id":"https://openalex.org/C56739046","wikidata":"https://www.wikidata.org/wiki/Q192060","display_name":"Knowledge management","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2586705","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586705","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W178420647","https://openalex.org/W1604936433","https://openalex.org/W2015983875","https://openalex.org/W2033008594","https://openalex.org/W2318189663","https://openalex.org/W2551720480","https://openalex.org/W4243780001"],"related_works":["https://openalex.org/W2368908306","https://openalex.org/W2886364346","https://openalex.org/W2089209555","https://openalex.org/W4313907067","https://openalex.org/W3192267411","https://openalex.org/W1989453270","https://openalex.org/W2256381225","https://openalex.org/W2479095697","https://openalex.org/W4292788325","https://openalex.org/W2952972631"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper":[3],"we":[4],"introduce":[5],"a":[6,55,79],"recursive":[7],"notation":[8,20],"system":[9,21,29],"O":[10,51,71],"(\u03a0":[11,52,72],"3":[12,40,53,60,63,73],")":[13,54,74],"of":[14,18,36,38,70],"ordinals.":[15],"An":[16],"element":[17],"the":[19,67],"is":[22,30,78],"called":[23],"an":[24],"ordinal":[25],"diagram":[26],".":[27],"The":[28],"designed":[31],"for":[32,45,61,85],"proof":[33],"theoretic":[34,83],"study":[35,84],"theories":[37,87],"\u03a0":[39,59,62],"-reflection.":[41],"We":[42],"show":[43],"that":[44,66],"each":[46],"\u03b1":[47,77],"&lt;":[48],"\u03a9":[49],"in":[50,91],"set":[56],"theory":[57],"KP":[58],"-reflection":[64],"proves":[65],"initial":[68],"segment":[69],"determined":[75],"by":[76],"well":[80],"ordering.":[81],"Proof":[82],"such":[86],"will":[88],"be":[89],"reported":[90],"[":[92],"4].":[93]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
