{"id":"https://openalex.org/W2106321875","doi":"https://doi.org/10.1017/s0960129513000856","title":"Realizability interpretation of PA by iterated limiting PCA","display_name":"Realizability interpretation of PA by iterated limiting PCA","publication_year":2014,"publication_date":"2014-03-11","ids":{"openalex":"https://openalex.org/W2106321875","doi":"https://doi.org/10.1017/s0960129513000856","mag":"2106321875"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129513000856","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0960129513000856","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/53D46311A574B495B399B826D9D4C6AA/S0960129513000856a.pdf/div-class-title-realizability-interpretation-of-pa-by-iterated-limiting-pca-div.pdf","source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"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":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/53D46311A574B495B399B826D9D4C6AA/S0960129513000856a.pdf/div-class-title-realizability-interpretation-of-pa-by-iterated-limiting-pca-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052310642","display_name":"Yohji Akama","orcid":"https://orcid.org/0000-0002-6652-7150"},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"YOHJI AKAMA","raw_affiliation_strings":["Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578Japan Email:","Mathematical Institute,Tohoku University,Aoba,Sendai,980-8578JapanEmail:akama@m.tohoku.ac.jp"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578Japan Email:","institution_ids":["https://openalex.org/I201537933"]},{"raw_affiliation_string":"Mathematical Institute,Tohoku University,Aoba,Sendai,980-8578JapanEmail:akama@m.tohoku.ac.jp","institution_ids":["https://openalex.org/I201537933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052310642"],"corresponding_institution_ids":["https://openalex.org/I201537933"],"apc_list":null,"apc_paid":null,"fwci":0.3656,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.65648855,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"24","issue":"6","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9991999864578247,"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":0.9977999925613403,"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":0.7855569124221802},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.6419345736503601},{"id":"https://openalex.org/keywords/partial-function","display_name":"Partial function","score":0.5888669490814209},{"id":"https://openalex.org/keywords/realizability","display_name":"Realizability","score":0.49828481674194336},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.49039721488952637},{"id":"https://openalex.org/keywords/partial-derivative","display_name":"Partial derivative","score":0.45398324728012085},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4446905255317688},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4410952627658844},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4310283958911896},{"id":"https://openalex.org/keywords/arithmetic-function","display_name":"Arithmetic function","score":0.42482858896255493},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15137097239494324},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08568426966667175},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07897204160690308}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7855569124221802},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.6419345736503601},{"id":"https://openalex.org/C182359184","wikidata":"https://www.wikidata.org/wiki/Q1756942","display_name":"Partial function","level":2,"score":0.5888669490814209},{"id":"https://openalex.org/C2776378722","wikidata":"https://www.wikidata.org/wiki/Q3454417","display_name":"Realizability","level":2,"score":0.49828481674194336},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.49039721488952637},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.45398324728012085},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4446905255317688},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4410952627658844},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4310283958911896},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.42482858896255493},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15137097239494324},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08568426966667175},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07897204160690308},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0960129513000856","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0960129513000856","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/53D46311A574B495B399B826D9D4C6AA/S0960129513000856a.pdf/div-class-title-realizability-interpretation-of-pa-by-iterated-limiting-pca-div.pdf","source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"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":"Mathematical Structures in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1307.5521","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1307.5521","pdf_url":"https://arxiv.org/pdf/1307.5521","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.744.3512","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.744.3512","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1307.5521.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1017/s0960129513000856","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0960129513000856","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/53D46311A574B495B399B826D9D4C6AA/S0960129513000856a.pdf/div-class-title-realizability-interpretation-of-pa-by-iterated-limiting-pca-div.pdf","source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"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":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2106321875.pdf","grobid_xml":"https://content.openalex.org/works/W2106321875.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W126568045","https://openalex.org/W1483568252","https://openalex.org/W1496947201","https://openalex.org/W1572451808","https://openalex.org/W1608607427","https://openalex.org/W1968638389","https://openalex.org/W1992845811","https://openalex.org/W1995881727","https://openalex.org/W2011841843","https://openalex.org/W2020510887","https://openalex.org/W2032172774","https://openalex.org/W2043566933","https://openalex.org/W2045304669","https://openalex.org/W2074872055","https://openalex.org/W2107359728","https://openalex.org/W2118633760","https://openalex.org/W2155384048","https://openalex.org/W2208743443","https://openalex.org/W4211036707","https://openalex.org/W4231545044","https://openalex.org/W4233830439","https://openalex.org/W4239934161","https://openalex.org/W4246886636","https://openalex.org/W4256423329","https://openalex.org/W6813216934"],"related_works":["https://openalex.org/W2535647996","https://openalex.org/W2109371256","https://openalex.org/W2162114838","https://openalex.org/W2184512187","https://openalex.org/W2279903697","https://openalex.org/W2073738669","https://openalex.org/W2116465509","https://openalex.org/W2391796915","https://openalex.org/W2370856440","https://openalex.org/W4210659825"],"abstract_inverted_index":{"For":[0],"any":[1,65,87],"partial":[2,15,37,43,48,69,89],"combinatory":[3],"algebra":[4],"(PCA":[5],"for":[6,106,121,132],"short)":[7,133],"$\\mathcal{A}$":[8,13,20,46],",":[9],"the":[10,23,35,41,73,77,95,99,113,140,149],"class":[11],"of":[12,25,28,45,56,76,102,125,156],"-representable":[14,47],"functions":[16,38,44,49],"from":[17],"$\\mathbb{N}$":[18,29],"to":[19,138],"quotiented":[21],"by":[22],"filter":[24],"cofinite":[26],"sets":[27],"is":[30,82,136,152],"a":[31,61,83],"PCA":[32,62,84,97],"such":[33],"that":[34,63,85],"representable":[36],"are":[39],"exactly":[40],"limiting":[42,68],"(Akama":[50],"2004).":[51],"The":[52],"n":[53,66,81,109],"-times":[54],"iteration":[55],"this":[57],"construction":[58],"results":[59],"in":[60],"represents":[64,86],"-iterated":[67],"recursive":[70],"function,":[71],"and":[72,111,134,148],"inductive":[74],"limit":[75],"PCAs":[78],"over":[79,94,112],"all":[80],"arithmetical":[88],"function.":[90],"Kleene's":[91],"realizability":[92],"interpretation":[93],"former":[96],"interprets":[98,117],"logical":[100,126],"principles":[101],"double":[103],"negation":[104],"elimination":[105],"\u03a3":[107],"0":[108],"-formulae,":[110],"latter":[114],"PCA,":[115],"it":[116],"Peano's":[118],"arithmetic":[119,130],"(PA":[120],"short).":[122],"A":[123],"hierarchy":[124],"systems":[127],"between":[128],"Heyting's":[129],"(HA":[131],"PA":[135],"used":[137],"discuss":[139],"prenex":[141],"normal":[142],"form":[143],"theorem,":[144],"relativised":[145],"independence-of-premise":[146],"schemes,":[147],"statement":[150],"\u2018PA":[151],"an":[153],"unbounded":[154],"extension":[155],"HA\u2019.":[157]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
