{"id":"https://openalex.org/W1527769569","doi":"https://doi.org/10.1007/3-540-45504-3_5","title":"Program Extraction from Gentzen\u2019s Proof of Transfinite Induction up to \u03b50","display_name":"Program Extraction from Gentzen\u2019s Proof of Transfinite Induction up to \u03b50","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1527769569","doi":"https://doi.org/10.1007/3-540-45504-3_5","mag":"1527769569"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-45504-3_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-45504-3_5","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5005999573","display_name":"Ulrich Berger","orcid":"https://orcid.org/0000-0002-7677-3582"},"institutions":[{"id":"https://openalex.org/I39586589","display_name":"Swansea University","ror":"https://ror.org/053fq8t95","country_code":"GB","type":"education","lineage":["https://openalex.org/I39586589"]},{"id":"https://openalex.org/I97429440","display_name":"University of Wales","ror":"https://ror.org/01se4f844","country_code":"GB","type":"education","lineage":["https://openalex.org/I97429440"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Ulrich Berger","raw_affiliation_strings":["Department of Computer Science, University of Wales Swansea, Singleton Park, Swansea, SA2 8PP, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Wales Swansea, Singleton Park, Swansea, SA2 8PP, UK","institution_ids":["https://openalex.org/I39586589","https://openalex.org/I97429440"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005999573"],"corresponding_institution_ids":["https://openalex.org/I39586589","https://openalex.org/I97429440"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10455105,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"68","last_page":"77"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9857000112533569,"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/T10317","display_name":"Advanced Database Systems and Queries","score":0.9710000157356262,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/transfinite-number","display_name":"Transfinite number","score":0.8763937950134277},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7839752435684204},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.610584557056427},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5853226780891418},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.5354685187339783},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.4974839985370636},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4948880076408386},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.4774399399757385},{"id":"https://openalex.org/keywords/mathematical-induction","display_name":"Mathematical induction","score":0.4728681743144989},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.46520525217056274},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4475128650665283},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4406796395778656},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.33285701274871826},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1188102662563324}],"concepts":[{"id":"https://openalex.org/C147358099","wikidata":"https://www.wikidata.org/wiki/Q1069891","display_name":"Transfinite number","level":2,"score":0.8763937950134277},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7839752435684204},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.610584557056427},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5853226780891418},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.5354685187339783},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.4974839985370636},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4948880076408386},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.4774399399757385},{"id":"https://openalex.org/C206743973","wikidata":"https://www.wikidata.org/wiki/Q178377","display_name":"Mathematical induction","level":2,"score":0.4728681743144989},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.46520525217056274},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4475128650665283},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4406796395778656},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33285701274871826},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1188102662563324},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-45504-3_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-45504-3_5","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W960388275","https://openalex.org/W1495212203","https://openalex.org/W1499154644","https://openalex.org/W1500868524","https://openalex.org/W1517093898","https://openalex.org/W1525064220","https://openalex.org/W1608607427","https://openalex.org/W1864285868","https://openalex.org/W2003467926","https://openalex.org/W2011606100","https://openalex.org/W2029816444","https://openalex.org/W2070702846","https://openalex.org/W2087334465","https://openalex.org/W2103403562","https://openalex.org/W2133262398","https://openalex.org/W2150899916","https://openalex.org/W2256089923","https://openalex.org/W2798718690","https://openalex.org/W3039529476","https://openalex.org/W4236380022","https://openalex.org/W4237376131"],"related_works":["https://openalex.org/W4381333853","https://openalex.org/W3005915128","https://openalex.org/W2243726694","https://openalex.org/W2584131834","https://openalex.org/W1937180777","https://openalex.org/W846236225","https://openalex.org/W2105747912","https://openalex.org/W169822098","https://openalex.org/W644998418","https://openalex.org/W3102144612"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}