{"id":"https://openalex.org/W2064269870","doi":"https://doi.org/10.2307/2274763","title":"Creativeness and completeness in recursion categories of partial recursive operators","display_name":"Creativeness and completeness in recursion categories of partial recursive operators","publication_year":1989,"publication_date":"1989-09-01","ids":{"openalex":"https://openalex.org/W2064269870","doi":"https://doi.org/10.2307/2274763","mag":"2064269870"},"language":"en","primary_location":{"id":"doi:10.2307/2274763","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274763","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":"Journal of Symbolic 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/A5109033991","display_name":"Franco Montagna","orcid":null},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Franco Montagna","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 di Siena, 53100 Siena, Italy","Universit\u00e0 Di Siena"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 di Siena, 53100 Siena, Italy","institution_ids":["https://openalex.org/I102064193"]},{"raw_affiliation_string":"Universit\u00e0 Di Siena","institution_ids":["https://openalex.org/I102064193"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068865870","display_name":"Andrea Sorbi","orcid":"https://orcid.org/0000-0001-9288-3290"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Andrea Sorbi","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 di Siena, 53100 Siena, Italy","Universit\u00e0 Di Siena"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 di Siena, 53100 Siena, Italy","institution_ids":["https://openalex.org/I102064193"]},{"raw_affiliation_string":"Universit\u00e0 Di Siena","institution_ids":["https://openalex.org/I102064193"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5081,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.74885896,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"54","issue":"3","first_page":"1023","last_page":"1041"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9896000027656555,"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":0.9896000027656555,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9771000146865845,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9745000004768372,"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":0.8388911485671997},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6355363726615906},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.6052963137626648},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5632702708244324},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5528801679611206},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5291840434074402},{"id":"https://openalex.org/keywords/double-recursion","display_name":"Double recursion","score":0.5132179260253906},{"id":"https://openalex.org/keywords/object","display_name":"Object (grammar)","score":0.5015347003936768},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.48058414459228516},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.44926732778549194},{"id":"https://openalex.org/keywords/mutual-recursion","display_name":"Mutual recursion","score":0.44385936856269836},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3423265218734741},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22622141242027283},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11474257707595825},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11106443405151367},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.07523933053016663}],"concepts":[{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.8388911485671997},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6355363726615906},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.6052963137626648},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5632702708244324},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5528801679611206},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5291840434074402},{"id":"https://openalex.org/C139503435","wikidata":"https://www.wikidata.org/wiki/Q5300083","display_name":"Double recursion","level":3,"score":0.5132179260253906},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.5015347003936768},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.48058414459228516},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.44926732778549194},{"id":"https://openalex.org/C124416688","wikidata":"https://www.wikidata.org/wiki/Q3454656","display_name":"Mutual recursion","level":3,"score":0.44385936856269836},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3423265218734741},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22622141242027283},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11474257707595825},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11106443405151367},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.07523933053016663},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2307/2274763","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274763","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":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183743038","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183743038","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:usiena-air.unisi.it:11365/1082634","is_oa":false,"landing_page_url":"http://hdl.handle.net/11365/1082634","pdf_url":null,"source":{"id":"https://openalex.org/S4377196319","display_name":"Use Siena air (University of Siena)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102064193","host_organization_name":"University of Siena","host_organization_lineage":["https://openalex.org/I102064193"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W83139932","https://openalex.org/W192846609","https://openalex.org/W1973392890","https://openalex.org/W1976065146","https://openalex.org/W2117832390","https://openalex.org/W2120713972","https://openalex.org/W2160625512","https://openalex.org/W2530006810","https://openalex.org/W2905135108","https://openalex.org/W4253210619"],"related_works":["https://openalex.org/W2006836388","https://openalex.org/W2896379815","https://openalex.org/W4249703975","https://openalex.org/W1563586960","https://openalex.org/W2374742784","https://openalex.org/W223586891","https://openalex.org/W2155605358","https://openalex.org/W560887346","https://openalex.org/W4246540581","https://openalex.org/W2044963554"],"abstract_inverted_index":{"Recursion":[0],"categories":[1],"have":[2],"been":[3],"proposed":[4],"by":[5,69],"Di":[6],"Paola":[7],"and":[8,29,143],"Heller":[9],"in":[10,22,42,52,65,87,131],"[DPH]":[11,66],"as":[12],"the":[13,23,44,71,116],"basis":[14],"for":[15,139],"a":[16,26,33,59,88,94,113,132],"category-theoretic":[17,55],"approach":[18],"to":[19,83,120,154],"recursion":[20,89,133],"theory,":[21],"context":[24],"of":[25,32,37,47,73,96,115],"more":[27],"general":[28],"ambitious":[30],"project":[31],"purely":[34],"algebraic":[35],"treatment":[36],"incompleteness":[38],"phenomena.":[39],"The":[40],"way":[41],"which":[43,79,149],"classical":[45,117],"notion":[46,72,95],"creative":[48,74,81,102,126,151],"set":[49,127],"is":[50,63,108,128,150,156],"rendered":[51],"this":[53],"new":[54],"framework":[56],"plays,":[57],"therefore,":[58],"central":[60],"role.":[61],"This":[62],"done":[64],"(Definition":[67],"8.1)":[68],"defining":[70],"domains":[75,78,103],"or,":[76],"rather,":[77],"are":[80],"relative":[82],"some":[84],"criterion:":[85],"thus,":[86],"category,":[90],"every":[91,125,140,147],"criterion":[92],"provides":[93],"creativeness.":[97],"A":[98],"basic":[99],"result":[100],"on":[101],"(cf.":[104],"[DPH,":[105],"Theorem":[106],"8.13])":[107],"that,":[109],"under":[110],"certain":[111],"assumptions,":[112],"version":[114],"result,":[118],"due":[119],"Myhill":[121],"[MYH],":[122],"stating":[123],"that":[124],"complete,":[129],"holds:":[130],"category":[134],"with":[135,152],"equality":[136],"(i.e.":[137],"exists":[138],"object":[141],"X)":[142],"having":[144],"enough":[145],"atoms,":[146],"domain":[148],"respect":[153],"atoms":[155],"also":[157],"complete.":[158]},"counts_by_year":[{"year":2016,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}