{“id”:“https://openalex.org/W1578684710“,”doi“:”https://doi.org/10.1007/978-3-540-73228-0-8“,”title“:“类型上带递推方程的\u03bb-演算的强正规化的算术证明”,“display_name”:“类型下带递推公式的\u02bb-演计算的强正规性的算术证明“,”publication_year“:2007,”publiation_date“:”2007-01-01“,”ids“:{”openalex“:”https://openalex.org/W1578684710“,”doi“:”https://doi.org/10.1007/978-3-540-73228-0_8“,”mag“:”1578684710“},”language“:”en“,”primary_location“:{”is_oa“:false,”landing_page_url“:”https://doi.org/10.1007/978-3-540-73228-0_8“,”pdf_url“:空,”源“:{”id“:”https://openalex.org/S106296714“,”display_name“:”计算机科学讲义“,”issn_l“:”0302-9743“,”issn“:[”0302-9743“,”1611-3349“],”is_oa“:false,”is_in_doaj“:false,”host_organization“:”https://openalex.org/P4310318900“,”“host_organization_name”:“Springer Science+Business Media”,“host_organization_lineage”:[“https://openalex.org/P431031965","https://openalex.org/P4310318900“],”host_organization_lineage_names“:[”Springer Nature“,”Springer-Science+Business Media“],“type”:“book-series”},“license”:null,“licence_id”:nul,“version”:null,“is_accepted”:false,“is_published”:false},”type“:”book-chapter“,”type_crossref“:“book-chapter”,”indexed_in“:[“crossref”],“open_access”:{“is_oa”:true,“oa_status”:“green”,“oa_url”:https://arxiv.org/pdf/0905.1032v1.pdf“,”any_repository_has_fulltext“:true},”authorships“:[{”author_position“:”第一“,”作者“:{”id“:”https://openalex.org/A5032263146“,”display_name“:”Ren\u00e9 David“,”orcid“:null},”institutions“:[{”id“:”https://openalex.org/I70900168“,”display_name“:”University\u00e9 Savoie Mont Blanc“,”ror“:”https://ror.org/04gqg1a07“,”country_code“:”FR“,”type“:“教育”,”世系“:[”https://openalex.org/I70900168“]}],”国家“:[”FR“],”is_corresponding“:false,”raw_author_name“:”Ren\u00e9 David“,”raw _ afiliation_strings“:[“University \u00e 9 de Savoie,Campus Scientifique,73376 Le Bourget du Lac,France”]},{“author_position”:“last”,“author”:{“id”:“https://openalex.org/A5018831581“,”display_name“:”Karim Nour“,”orcid“:”https://orcid.org/0000-0003-1943-272X},“机构”:[{“id”:https://openalex.org/I70900168“,”display_name“:”University\u00e9 Savoie Mont Blanc“,”ror“:”https://ror.org/04gqg1a07“,”country_code“:”FR“,”type“:“教育”,”世系“:[”https://openalex.org/I70900168“]}],”国家“:[”FR“],”is_corresponding“:false,”raw_author_name“:”Karim Nour“,”raw _affiliation_strings“:[“University\u00e9 de Savoie,Campus Scientifique,73376 Le Bourget du Lac,France”]],”countries_distiction_count“:1,”institutions_distinact_count{“值”:5000,“货币“:”EUR“,”value_usd“:5392,”出处“:”doaj“},”apc_payed“:{”value“:5000,”货币“:“EUR”,“value_usd:5392,“出处”:“doaj”},“has_fulltext”:true,“fulltext_origin”:“ngrams”,“cited_by_count”:1,“cited_by_percentile_year”:{“min”:66,“max”:73},,“biblio”:{“volume”:null,“issue”:null,“first_page”:“84”,“last_page”:“101”},“is_retracted”:false,“is_paratext“:false,”primary_topic“:{”id“:”https://openalex.org/T10126“,”display_name“:”程序分析和验证技术“,”score“:0.9998,”subfield“:{”id“:”https://openalex.org/subfields/1702“,”display_name“:”人工智能“},”字段“:{”id“:”https://openalex.org/fields/17“,”display_name“:”Computer Science“},”domain“:{”id“:”https://openalex.org/domains/3“,”display_name“:”物理科学“}},”主题“:[{”id“:”https://openalex.org/T10126“,”display_name“:”程序分析和验证技术“,”score“:0.9998,”subfield“:{”id“:”https://openalex.org/subfields/1702“,”display_name“:”人工智能“},”字段“:{”id“:”https://openalex.org/fields/17“,”display_name“:”Computer Science“},”domain“:{”id“:”https://openalex.org/domains/3“,”display_name“:”物理科学“}},{”id“:”https://openalex.org/T11010“,”display_name“:”逻辑编程与知识表示“,”score“:0.9991,”subfield“:{”id“:”https://openalex.org/subfields/1702“,”display_name“:”人工智能“},”字段“:{”id“:”https://openalex.org/fields/17“,”display_name“:”Computer Science“},”domain“:{”id“:”https://openalex.org/domains/3“,”display_name“:”物理科学“}},{”id“:”https://openalex.org/T10142“,”“display_name”:“软件验证和控制中的形式方法”,“score”:0.9788,“subfield”:{“id”:“https://openalex.org/subfields/1703“,”display_name“:”计算理论与数学“},”字段“:{”id“:”https://openalex.org/fields/17“,”display_name“:”Computer Science“},”domain“:{”id“:”https://openalex.org/domains/3“,”display_name“:”物理科学“}}],”关键词“:[{”id“:”https://openalex.org/keywords/model-checking“,”display_name“:”模型检查“,”score“:0.492772}],”concepts“:[{”id“:”https://openalex.org/C97489613,“wikidata”:https://www.wikidata.org/wiki/Q842755“,”display_name“:”皮亚诺公理“,”level“:2,”score“:0.86839545},{”id“:”https://openalex.org/C112343008,“wikidata”:https://www.wikidata.org/wiki/Q140744“,”display_name“:”算术函数“,”level“:2,”score“:0.74950373},{”id“:”https://openalex.org/C136886441,“wikidata”:https://www.wikidata.org/wiki/Q926129“,”display_name“:”规范化(社会学)“,”level“:2,”score“:0.74095875},{”id“:”https://openalex.org/C2777686260,“wikidata”:https://www.wikidata.org/wiki/Q144037“,”display_name“:”微积分(牙科)“,”level“:2,”score“:0.58732516},{”id“:”https://openalex.org/C195653647,“wikidata”:https://www.wikidata.org/wiki/Q7625047“,”display_name“:”结构证明理论“,”level“:4,”score“:0.5461808},{”id“:”https://openalex.org/C33923547,“wikidata”:https://www.wikidata.org/wiki/Q395“,”display_name“:”数学“,”等级“:0,”分数“:0.50188446},{”id“:”https://openalex.org/C159333733,“wikidata”:https://www.wikidata.org/wiki/Q7051809“,”display_name“:”规范化属性“,”level“:2,”score“:0.45719185},{”id“:”https://openalex.org/C2780586882,“wikidata”:https://www.wikidata.org/wiki/Q7520643“,”display_name“:”简单(哲学)“,”level“:2,”score“:0.4414174},{”id“:”https://openalex.org/C93682546,“wikidata”:https://www.wikidata.org/wiki/Q1056428“,”display_name“:”类型理论“,”level“:3,”score“:0.44021896},{”id“:”https://openalex.org/C33695381,“wikidata”:https://www.wikidata.org/wiki/Q7804838“,”display_name“:”时间刻度演算“,”level“:3,”score“:0.43956855},{”id“:”https://openalex.org/C136119220,“wikidata”:https://www.wikidata.org/wiki/Q1000660“,”“display_name”“:”“域上的代数”“,”level“:2,”score“:0.42972687},{”id“:”https://openalex.org/C2318724,“wikidata”:https://www.wikidata.org/wiki/Q852732“,”display_name“:”证明理论“,”level“:3,”score“:0.38802275},{”id“:”https://openalex.org/C41008148,“wikidata”:https://www.wikidata.org/wiki/Q21198(网址:https://www.wikidata.org/wiki/Q21198)“,”display_name“:”计算机科学“,”level“:0,”score“:0.3875457},{”id“:”https://openalex.org/C118615104,“wikidata”:https://www.wikidata.org/wiki/Q121416“,”display_name“:”离散数学“,”level“:1,”score“:0.34781894},{”id“:”https://openalex.org/C2777299769,“wikidata”:https://www.wikidata.org/wiki/Q3707858“,”display_name“:”Type(biology)“,”level“:2,”score“:0.25413513},{”id“:”https://openalex.org/C108710211,“wikidata”:https://www.wikidata.org/wiki/Q11538“,”display_name“:”数学证明“,”level“:2,”score“:0.2431137},{”id“:”https://openalex.org/C202444582,“wikidata”:https://www.wikidata.org/wiki/Q837863“,”display_name“:”纯数学“,”level“:1,”score“:0.2594627},{”id“:”https://openalex.org/C117312493,“wikidata”:https://www.wikidata.org/wiki/Q2035437“,”display_name“:”多元微积分“,”level“:2,”score“:0.097538054},{”id“:”https://openalex.org/C199360897,“wikidata”:https://www.wikidata.org/wiki/Q9143“,”display_name“:”编程语言“,”level“:1,”score“:0.05225703},{”id“:”https://openalex.org/C138885662,“wikidata”:https://www.wikidata.org/wiki/Q5891“,”display_name“:”哲学“,”等级“:0,”分数“:0.0},{”id“:”https://openalex.org/C199343813,“wikidata”:https://www.wikidata.org/wiki/Q12128“,”display_name“:”牙科“,”level“:1,”score“:0.0},{”id“:”https://openalex.org/C19165224,“wikidata”:https://www.wikidata.org/wiki/Q23404(网址:https://www.wikidata.org/wiki/Q23404)“,”display_name“:”人类学“,”level“:1,”score“:0.0},{”id“:”https://openalex.org/C144024400,“wikidata”:https://www.wikidata.org/wiki/Q21201“,”display_name“:”社会学“,”level“:0,”score“:0.0},{”id“:”https://openalex.org/C127413603,“wikidata”:https://www.wikidata.org/wiki/Q11023“,”display_name“:”工程“,”级别“:0,”分数“:0.0},{”id“:”https://openalex.org/C2524010,“wikidata”:https://www.wikidata.org/wiki/Q8087“,”display_name“:”Geometry“,”level“:1,”score“:0.0},{”id“:”https://openalex.org/C111472728,“wikidata”:https://www.wikidata.org/wiki/Q9471“,”display_name“:”认识论“,”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},{”id“:”https://openalex.org/C133731056,“wikidata”:https://www.wikidata.org/wiki/Q4917288“,”display_name“:”控制工程“,”level“:1,”score“:0.0},{”id“:”https://openalex.org/C18903297,“wikidata”:https://www.wikidata.org/wiki/Q7150“,”display_name“:”生态学“,”level“:1,”score“:0.0},{”id“:”https://openalex.org/C86803240,“wikidata”:https://www.wikidata.org/wiki/Q420“,”display_name“:”Biology“,”level“:0,”score“:0.0}],”mesh“:[],”locations_count“:2,”location“:[{”is_oa“:false,”landing_page_url“:”https://doi.org/10.1007/978-3-540-73228-0_8“,”pdf_url“:空,”源“:{”id“:”https://openalex.org/S106296714“,”“display_name”“:”“计算机科学课堂讲稿”“,”issn_l“:”0302-9743“,”isn“:[”0302-7743“、”1611-3349“],”is_oa“:false,”is_in_doaj“:false,”host_organization“:”https://openalex.org/P4310318900“,”“host_organization_name”:“Springer Science+Business Media”,“host_organization_lineage”:[“https://openalex.org/P431031965","https://openalex.org/P4310318900“],”host_organization_lineage_names“:[”Springer Nature“,”Springer-Science+Business Media“],“type”:“book-series”},“license”:null,“licence_id”:nul,“version”:null,“is_accepted”:false,“is_published”:false},{“is_oa”:true,“landing_page_url”:nuld,“pdf_url“:”https://arxiv.org/pdf/0905.1032v1.pdf,“源”:{“id”:https://openalex.org/S4306400194“,”display_name“:”arXiv(康奈尔大学)“,”issn_l“:null,”issn“:null,”is_oa“:true,”is_ in_doaj“:false,”host_organization“:”https://openalex.org/I205783295“,”“host_organization_name”:“康奈尔大学”,“host_organization_lineage”:[“https://openalex.org/I205783295“],”host_organization_lineage_names“:[”康奈尔大学“],”type“:”repository“},”license“:null,”license_id“:null,”version“:”submittedVersion“,”is_accepted“:false,”is_published“:false}],”best_oa_location“:{”is_oa“:true,”landing_page_url“:null,”pdf_url“:”https://arxiv.org/pdf/0905.1032v1.pdf,“源”:{“id”:https://openalex.org/S4306400194“,”display_name“:”arXiv(康奈尔大学)“,”issn_l“:null,”issn“:null,”is_oa“:true,”is_ in_doaj“:false,”host_organization“:”https://openalex.org/I205783295“,”“host_organization_name”:“康奈尔大学”,“host_organization_lineage”:[“https://openalex.org/I205783295“],”host_organization_lineage_names“:[”康奈尔大学“],“type”:“repository”},“license”:null,“licence_id”:null,“version”:“submittedVersion”,“is_accepted”:false,“is_published”:false},”sustainable_development_goals“:[],“grants”:[]、“datasets”:【】,“versions”:【],“referenced_works_count”:31,“referrenced_works”:[”https://openalex.org/W124154939","https://openalex.org/W1456004531","https://openalex.org/W1494376884","https://openalex.org/W1501048703","https://openalex.org/W1501402401","https://openalex.org/W1525064220网址","https://openalex.org/W1534493251","https://openalex.org/W1591846509","https://openalex.org/W1981303668","https://openalex.org/W1986402635","https://openalex.org/W1991947308","https://openalex.org/W1996404651","https://openalex.org/W2002293839","https://openalex.org/W2003295197","https://openalex.org/W2007974484","https://openalex.org/W2011359032","https://openalex.org/W2023266231","https://openalex.org/W2027585565","https://openalex.org/W2045427966","https://openalex.org/W2059054133","https://openalex.org/W2095405219","https://openalex.org/W2132936218","https://openalex.org/W2141636159","https://openalex.org/W2145123272","https://openalex.org/W2149837936","https://openalex.org/W2154273644","https://openalex.org/W2220986375","https://openalex.org/W2319619459","https://openalex.org/W2334137773","https://openalex.org/W277331151","https://openalex.org/W4388310127“],”related_works“:[”https://openalex.org/W4320723398","https://openalex.org/W3134370287","https://openalex.org/W3105768380","https://openalex.org/W2188987066","https://openalex.org/W2166197034","https://openalex.org/W2123497262","https://openalex.org/W2033339909","https://openalex.org/W1994341859","https://openalex.org/W1833447734","https://openalex.org/W169822098“],”ngrams_url“:”https://api.openalex.org/works/W1578684710/ngrams“,”abstract_inverted_index“:{”We“:[0],”give“:[1],”an“:[2,39],”算术“:[3],”证明“:[4,33,49,65,70],”of“:[5,9,14,24,36,42,58],”the“:[6,10,15,18,22,43,59],”strong“:[7],”normalization“:[8],”\u03bb-calculus“:[11],”(and“:[12],”also“:[13],”\ u03bb\u 03bc-calculus)“:[16],”其中“:[17],”类型“:[19],”系统“:[20,60],”是“:[21,38,74],”一“:[23,44],”简单“:[25],“类型”:[26],“with”:[27],“recursive”:[28],“quations”:[29,46],“on”:[30],“types”。“:[31],”The“:[32,56],”using“:[34],”candidates“:[35],”reducibility“:[37],”easy“:[40],”extension“:[41],”without“:[45],”but“,”this“:48],”can“:[50],”be“:[51],”formalized“:[52],”in“:[53],”Peano“:[54,78],”algorithmic“。“:[55,79],”强度“:[57],”需要“:[61],”对于“:[62],”这样“:[63],”a“:[64],”是“:[66],”不是“:[67,75],”已知。“:[68],”Our“:[69],”shows“:[71],”that“:[72],”it“:[73],”more“:[76],”than“:[77]},”cited_by_api_url“:”https://api.openalex.org/works?filter=cites:W1578684710“,”counts_by_year“:[],”updated_date“:”2024-05-10T15:12:25.198610“,”created_dates“:”2016-06-24“}“