{"id":"https://openalex.org/W2093232417","doi":"https://doi.org/10.1016/s0168-0072(03)00020-4","title":"Proof theory for theories of ordinals\u2014I: recursively Mahlo ordinals","display_name":"Proof theory for theories of ordinals\u2014I: recursively Mahlo ordinals","publication_year":2003,"publication_date":"2003-06-30","ids":{"openalex":"https://openalex.org/W2093232417","doi":"https://doi.org/10.1016/s0168-0072(03)00020-4","mag":"2093232417"},"language":"en","primary_location":{"id":"doi:10.1016/s0168-0072(03)00020-4","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0168-0072(03)00020-4","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0168007203000204/pdf","source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.sciencedirect.com/science/article/pii/S0168007203000204/pdf","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/I65837984","display_name":"Kobe University","ror":"https://ror.org/03tgsfw79","country_code":"JP","type":"education","lineage":["https://openalex.org/I65837984"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Toshiyasu Arai","raw_affiliation_strings":["Graduate School of Science and Technology, Kobe University, Rokko-dai, Nada-ku, Kobe 657-8501, Japan","Graduate School of Science and Technology, Kobe University, Rokko-Dai, Nada-Ku Kobe 657-8501, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Science and Technology, Kobe University, Rokko-dai, Nada-ku, Kobe 657-8501, Japan","institution_ids":["https://openalex.org/I65837984"]},{"raw_affiliation_string":"Graduate School of Science and Technology, Kobe University, Rokko-Dai, Nada-Ku Kobe 657-8501, Japan","institution_ids":["https://openalex.org/I65837984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110301130"],"corresponding_institution_ids":["https://openalex.org/I65837984"],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":null,"fwci":1.8248,"has_fulltext":true,"cited_by_count":34,"citation_normalized_percentile":{"value":0.85460045,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"122","issue":"1-3","first_page":"1","last_page":"85"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9976000189781189,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9976000189781189,"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":0.9922000169754028,"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":0.9843000173568726,"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/mathematics","display_name":"Mathematics","score":0.7792414426803589},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.6837002038955688},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5184144973754883},{"id":"https://openalex.org/keywords/structural-proof-theory","display_name":"Structural proof theory","score":0.5032591223716736},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.45339468121528625},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3682723641395569},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3507940173149109},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.23389309644699097},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.055516213178634644}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7792414426803589},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.6837002038955688},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5184144973754883},{"id":"https://openalex.org/C195653647","wikidata":"https://www.wikidata.org/wiki/Q7625047","display_name":"Structural proof theory","level":4,"score":0.5032591223716736},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.45339468121528625},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3682723641395569},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3507940173149109},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.23389309644699097},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.055516213178634644},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0168-0072(03)00020-4","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0168-0072(03)00020-4","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0168007203000204/pdf","source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/s0168-0072(03)00020-4","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0168-0072(03)00020-4","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0168007203000204/pdf","source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2093232417.pdf","grobid_xml":"https://content.openalex.org/works/W2093232417.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W40029885","https://openalex.org/W56017028","https://openalex.org/W178420647","https://openalex.org/W1587799979","https://openalex.org/W1809068920","https://openalex.org/W1890908087","https://openalex.org/W2063028251","https://openalex.org/W2064023341","https://openalex.org/W2064882914","https://openalex.org/W2152822550","https://openalex.org/W2217500413","https://openalex.org/W2475785644","https://openalex.org/W3039529476","https://openalex.org/W4293117209","https://openalex.org/W6602295131","https://openalex.org/W6638419616","https://openalex.org/W6639527600","https://openalex.org/W6688251936"],"related_works":["https://openalex.org/W1558859407","https://openalex.org/W2481254132","https://openalex.org/W2770391921","https://openalex.org/W1528233644","https://openalex.org/W2953934790","https://openalex.org/W2771528016","https://openalex.org/W2804296252","https://openalex.org/W4289719525","https://openalex.org/W2964922400","https://openalex.org/W4287024315"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-08-02T14:50:37.381335","created_date":"2025-10-10T00:00:00"}