{"id":"https://openalex.org/W1998796136","doi":"https://doi.org/10.1016/0168-0072(94)00003-l","title":"Elementary descent recursion and proof theory","display_name":"Elementary descent recursion and proof theory","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W1998796136","doi":"https://doi.org/10.1016/0168-0072(94)00003-l","mag":"1998796136"},"language":"en","primary_location":{"id":"doi:10.1016/0168-0072(94)00003-l","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0168-0072(94)00003-l","pdf_url":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046248935","display_name":"Harvey M. Friedman","orcid":"https://orcid.org/0000-0002-0765-9460"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Harvey Friedman","raw_affiliation_strings":["Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210-1174, USA","Department of Mathematics; The Ohio State University; 231 West 18th Avenue Columbus OH 43210-1174 USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210-1174, USA","institution_ids":["https://openalex.org/I52357470"]},{"raw_affiliation_string":"Department of Mathematics; The Ohio State University; 231 West 18th Avenue Columbus OH 43210-1174 USA","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113481835","display_name":"Michael Sheard","orcid":null},"institutions":[{"id":"https://openalex.org/I100236772","display_name":"St. Lawrence University","ror":"https://ror.org/05pvqha70","country_code":"US","type":"education","lineage":["https://openalex.org/I100236772"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael Sheard","raw_affiliation_strings":["Department of Mathematics, St. Lawrence University, Canton, NY 13617, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, St. Lawrence University, Canton, NY 13617, USA","institution_ids":["https://openalex.org/I100236772"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5113481835"],"corresponding_institution_ids":["https://openalex.org/I100236772"],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":null,"fwci":7.6302,"has_fulltext":false,"cited_by_count":61,"citation_normalized_percentile":{"value":0.97100654,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"71","issue":"1","first_page":"1","last_page":"45"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9915000200271606,"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":0.9915000200271606,"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":0.9879000186920166,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9869999885559082,"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/recursion","display_name":"Recursion (computer science)","score":0.7559725046157837},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6997441053390503},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6141940355300903},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.6024501323699951},{"id":"https://openalex.org/keywords/primitive-recursive-function","display_name":"Primitive recursive function","score":0.5483891367912292},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5359194278717041},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.529303789138794},{"id":"https://openalex.org/keywords/recursive-functions","display_name":"Recursive functions","score":0.4734477698802948},{"id":"https://openalex.org/keywords/\u03bc-operator","display_name":"\u03bc operator","score":0.45054730772972107},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4340210556983948},{"id":"https://openalex.org/keywords/analytic-proof","display_name":"Analytic proof","score":0.41625362634658813},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38841867446899414},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24597612023353577},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23858067393302917},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22983422875404358},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.1401730477809906},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.12311017513275146},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07307246327400208}],"concepts":[{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.7559725046157837},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6997441053390503},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6141940355300903},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.6024501323699951},{"id":"https://openalex.org/C9986523","wikidata":"https://www.wikidata.org/wiki/Q1570472","display_name":"Primitive recursive function","level":2,"score":0.5483891367912292},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5359194278717041},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.529303789138794},{"id":"https://openalex.org/C2982939207","wikidata":"https://www.wikidata.org/wiki/Q1175101","display_name":"Recursive functions","level":2,"score":0.4734477698802948},{"id":"https://openalex.org/C85955891","wikidata":"https://www.wikidata.org/wiki/Q307772","display_name":"\u03bc operator","level":3,"score":0.45054730772972107},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4340210556983948},{"id":"https://openalex.org/C135754263","wikidata":"https://www.wikidata.org/wiki/Q4751136","display_name":"Analytic proof","level":3,"score":0.41625362634658813},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38841867446899414},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24597612023353577},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23858067393302917},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22983422875404358},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.1401730477809906},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.12311017513275146},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07307246327400208},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0168-0072(94)00003-l","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0168-0072(94)00003-l","pdf_url":null,"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":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.6000000238418579}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W198973586","https://openalex.org/W1539702044","https://openalex.org/W1579247651","https://openalex.org/W2071823993","https://openalex.org/W2074448200","https://openalex.org/W2988584482","https://openalex.org/W3038873949","https://openalex.org/W3039529476","https://openalex.org/W3043060850","https://openalex.org/W6608186297","https://openalex.org/W6634526445","https://openalex.org/W6769935027"],"related_works":["https://openalex.org/W1596057910","https://openalex.org/W2368379187","https://openalex.org/W4239583161","https://openalex.org/W2055746193","https://openalex.org/W252215219","https://openalex.org/W3102439663","https://openalex.org/W1589207578","https://openalex.org/W4239039951","https://openalex.org/W2147242574","https://openalex.org/W4251662928"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}