{"id":"https://openalex.org/W1970069956","doi":"https://doi.org/10.2178/jsl/1254748682","title":"Functional interpretation and inductive definitions","display_name":"Functional interpretation and inductive definitions","publication_year":2009,"publication_date":"2009-10-05","ids":{"openalex":"https://openalex.org/W1970069956","doi":"https://doi.org/10.2178/jsl/1254748682","mag":"1970069956"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1254748682","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1254748682","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":"The Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://figshare.com/articles/Functional_Interpretation_and_Inductive_Definitions/6491660","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003483051","display_name":"Jeremy Avigad","orcid":"https://orcid.org/0000-0003-1275-315X"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jeremy Avigad","raw_affiliation_strings":["Department of Philosophy and Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pa 15213, USA, E-mail:","Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Philosophy and Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pa 15213, USA, E-mail:","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047471753","display_name":"Henry Towsner","orcid":"https://orcid.org/0000-0001-7993-5148"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]},{"id":"https://openalex.org/I2803209242","display_name":"University of California System","ror":"https://ror.org/00pjdza24","country_code":"US","type":"education","lineage":["https://openalex.org/I2803209242"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Henry Towsner","raw_affiliation_strings":["University of California, Los Angeles 520 Portola Plaza Math Sciences Building 6363 Mailcode: 155505 Los Angeles, Ca 90095, USA, E-mail:","University of California"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Los Angeles 520 Portola Plaza Math Sciences Building 6363 Mailcode: 155505 Los Angeles, Ca 90095, USA, E-mail:","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"University of California","institution_ids":["https://openalex.org/I2803209242"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.411,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.80272215,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"74","issue":"4","first_page":"1100","last_page":"1120"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9970999956130981,"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":0.9970999956130981,"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":0.9958999752998352,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9941999912261963,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/transfinite-number","display_name":"Transfinite number","score":0.8972359895706177},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.8378313779830933},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.7034183740615845},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5319376587867737},{"id":"https://openalex.org/keywords/inductive-reasoning","display_name":"Inductive reasoning","score":0.48619502782821655},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4403045177459717},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3778533935546875},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3441377282142639},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.25322532653808594},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21973443031311035},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1971520483493805},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09017258882522583},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.056266844272613525}],"concepts":[{"id":"https://openalex.org/C147358099","wikidata":"https://www.wikidata.org/wiki/Q1069891","display_name":"Transfinite number","level":2,"score":0.8972359895706177},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.8378313779830933},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.7034183740615845},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5319376587867737},{"id":"https://openalex.org/C21563000","wikidata":"https://www.wikidata.org/wiki/Q484511","display_name":"Inductive reasoning","level":2,"score":0.48619502782821655},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4403045177459717},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3778533935546875},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3441377282142639},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25322532653808594},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21973443031311035},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1971520483493805},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09017258882522583},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.056266844272613525},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":13,"locations":[{"id":"doi:10.2178/jsl/1254748682","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1254748682","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":"The Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:figshare.com:article/6491660","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Functional_Interpretation_and_Inductive_Definitions/6491660","pdf_url":"https://figshare.com/articles/Functional_Interpretation_and_Inductive_Definitions/6491660","source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:repository.cmu.edu:philosophy-1023","is_oa":false,"landing_page_url":"http://repository.cmu.edu/cgi/viewcontent.cgi?article=1023&context=philosophy","pdf_url":null,"source":{"id":"https://openalex.org/S4306400668","display_name":"Research Showcase @ Carnegie Mellon University (Carnegie Mellon University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74973139","host_organization_name":"Carnegie Mellon University","host_organization_lineage":["https://openalex.org/I74973139"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of Philosophy","raw_type":"text"},{"id":"pmh:doi:10.1184/r1/6491660","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Journal contribution"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1254748682","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1254748682","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.243.1062","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.243.1062","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/0802.1938v4.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.243.2283","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.243.2283","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/0802.1938v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.243.2521","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.243.2521","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/0802.1938v3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.243.4775","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.243.4775","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/0802.1938v2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.359.6735","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.359.6735","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.644.6661","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.644.6661","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.820.3239","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.820.3239","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://repository.cmu.edu/cgi/viewcontent.cgi?article%3D1023%26context%3Dphilosophy","raw_type":"text"},{"id":"doi:10.1184/r1/6491660.v1","is_oa":true,"landing_page_url":"https://doi.org/10.1184/r1/6491660.v1","pdf_url":null,"source":{"id":"https://openalex.org/S7407050927","display_name":"KiltHub Repository","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"JournalArticle"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/6491660","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Functional_Interpretation_and_Inductive_Definitions/6491660","pdf_url":"https://figshare.com/articles/Functional_Interpretation_and_Inductive_Definitions/6491660","source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1970069956.pdf"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W87922972","https://openalex.org/W110027972","https://openalex.org/W162931075","https://openalex.org/W165729215","https://openalex.org/W198905792","https://openalex.org/W561202933","https://openalex.org/W1446225236","https://openalex.org/W1485672136","https://openalex.org/W1498439614","https://openalex.org/W1507970960","https://openalex.org/W1525064220","https://openalex.org/W1559609146","https://openalex.org/W1579817075","https://openalex.org/W1591883570","https://openalex.org/W1793763201","https://openalex.org/W1893170605","https://openalex.org/W1965517429","https://openalex.org/W1975734325","https://openalex.org/W1996932891","https://openalex.org/W2008158074","https://openalex.org/W2041461531","https://openalex.org/W2064201145","https://openalex.org/W2079521728","https://openalex.org/W2085869400","https://openalex.org/W2097978997","https://openalex.org/W2163947143","https://openalex.org/W2272162156","https://openalex.org/W2516566257","https://openalex.org/W2734815139","https://openalex.org/W2977904728","https://openalex.org/W6741054553"],"related_works":["https://openalex.org/W3125250027","https://openalex.org/W1998092208","https://openalex.org/W1904838180","https://openalex.org/W4243085715","https://openalex.org/W1864285868","https://openalex.org/W2952039605","https://openalex.org/W1996319902","https://openalex.org/W2041590892","https://openalex.org/W1970069956","https://openalex.org/W2177196084"],"abstract_inverted_index":{"Abstract":[0],"Extending":[1],"G\u00f6del's":[2],"Dialectica":[3],"interpretation,":[4],"we":[5],"provide":[6],"a":[7],"functional":[8],"interpretation":[9],"of":[10,13,22],"classical":[11],"theories":[12,21],"positive":[14],"arithmetic":[15],"inductive":[16],"definitions,":[17],"reducing":[18],"them":[19],"to":[20],"finite-type":[23],"functionals":[24],"defined":[25],"using":[26],"transfinite":[27],"recursion":[28],"on":[29],"well-founded":[30],"trees.":[31]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-01T08:55:40.977307","created_date":"2025-10-10T00:00:00"}