{"id":"https://openalex.org/W2089259606","doi":"https://doi.org/10.2307/420945","title":"The Mathematical Work of S.C.Kleene","display_name":"The Mathematical Work of S.C.Kleene","publication_year":1995,"publication_date":"1995-03-01","ids":{"openalex":"https://openalex.org/W2089259606","doi":"https://doi.org/10.2307/420945","mag":"2089259606"},"language":"en","primary_location":{"id":"doi:10.2307/420945","is_oa":false,"landing_page_url":"https://doi.org/10.2307/420945","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"Bulletin 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/A5052883933","display_name":"J. R. Shoenfield","orcid":null},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"J.R. Shoenfield","raw_affiliation_strings":["Duke University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Duke University","institution_ids":["https://openalex.org/I170897317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052883933"],"corresponding_institution_ids":["https://openalex.org/I170897317"],"apc_list":null,"apc_paid":null,"fwci":2.1088,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.87413541,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"1","issue":"1","first_page":"9","last_page":"43"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.991100013256073,"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/T11567","display_name":"semigroups and automata theory","score":0.9866999983787537,"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/computability-theory","display_name":"Computability theory","score":0.722527027130127},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6837587952613831},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.6813107132911682},{"id":"https://openalex.org/keywords/computable-function","display_name":"Computable function","score":0.6105056405067444},{"id":"https://openalex.org/keywords/successor-cardinal","display_name":"Successor cardinal","score":0.6047846674919128},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5330919623374939},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.509046733379364},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3996528387069702},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39612680673599243},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.3247791528701782},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32043910026550293},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2756611108779907},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19428256154060364},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.19279363751411438}],"concepts":[{"id":"https://openalex.org/C111142201","wikidata":"https://www.wikidata.org/wiki/Q818930","display_name":"Computability theory","level":2,"score":0.722527027130127},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6837587952613831},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.6813107132911682},{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.6105056405067444},{"id":"https://openalex.org/C75306776","wikidata":"https://www.wikidata.org/wiki/Q7632662","display_name":"Successor cardinal","level":2,"score":0.6047846674919128},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5330919623374939},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.509046733379364},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3996528387069702},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39612680673599243},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.3247791528701782},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32043910026550293},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2756611108779907},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19428256154060364},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.19279363751411438},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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:10.2307/420945","is_oa":false,"landing_page_url":"https://doi.org/10.2307/420945","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"Bulletin of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.bsl/1181153982","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bsl/1181153982","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:10.1.1.27.4661","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.4661","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucla.edu/~asl/bsl/0101/0101-003.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W6754198","https://openalex.org/W174270456","https://openalex.org/W656682580","https://openalex.org/W883393071","https://openalex.org/W1042815620","https://openalex.org/W1153502047","https://openalex.org/W1484625174","https://openalex.org/W1485161910","https://openalex.org/W1486610321","https://openalex.org/W1523047387","https://openalex.org/W1526907582","https://openalex.org/W1529074087","https://openalex.org/W1566235828","https://openalex.org/W1964062928","https://openalex.org/W1967629533","https://openalex.org/W1983523043","https://openalex.org/W1993857645","https://openalex.org/W1994655624","https://openalex.org/W1996932891","https://openalex.org/W1999479735","https://openalex.org/W1999737391","https://openalex.org/W2013146192","https://openalex.org/W2014540725","https://openalex.org/W2023778211","https://openalex.org/W2033831013","https://openalex.org/W2035184507","https://openalex.org/W2036869460","https://openalex.org/W2040094858","https://openalex.org/W2042499838","https://openalex.org/W2043566933","https://openalex.org/W2045033949","https://openalex.org/W2045847292","https://openalex.org/W2056414301","https://openalex.org/W2069070044","https://openalex.org/W2069450525","https://openalex.org/W2081416038","https://openalex.org/W2085041816","https://openalex.org/W2085869400","https://openalex.org/W2087443598","https://openalex.org/W2242448088","https://openalex.org/W2315610131","https://openalex.org/W2319210160","https://openalex.org/W2320296823","https://openalex.org/W2325612495","https://openalex.org/W2325991838","https://openalex.org/W2328992634","https://openalex.org/W2611024016","https://openalex.org/W2736186402","https://openalex.org/W4232277851","https://openalex.org/W4236269533","https://openalex.org/W4239828288","https://openalex.org/W4255968424"],"related_works":["https://openalex.org/W1555412307","https://openalex.org/W2133902039","https://openalex.org/W4247585886","https://openalex.org/W596942210","https://openalex.org/W2936847277","https://openalex.org/W4388310202","https://openalex.org/W4243200898","https://openalex.org/W2310420552","https://openalex.org/W2359098868","https://openalex.org/W1792924550"],"abstract_inverted_index":{"\u00a71.":[0],"The":[1],"origins":[2],"of":[3,44,55,83,101,108,111,133,156,159,171,204,216,223],"recursion":[4,23],"theory":[5,24,29,107,120],".":[6],"In":[7,153],"dedicating":[8],"a":[9,26,105,140,157,169],"book":[10],"to":[11,16,63,74,98,117,124,143],"Steve":[12],"Kleene,":[13],"I":[14],"referred":[15],"him":[17],"as":[18,66],"the":[19,42,53,81,109,112,134,176,183,187],"person":[20],"who":[21,39],"made":[22],"into":[25],"theory.":[27],"Recursion":[28],"was":[30,52,87,206],"begun":[31],"by":[32],"Kleene's":[33],"teacher":[34],"at":[35],"Princeton,":[36],"Alonzo":[37],"Church,":[38],"first":[40,47,70],"defined":[41],"class":[43,51,54,170,203],"recursive":[45,113,144],"functions;":[46],"maintained":[48],"that":[49,182,201],"this":[50,72,119,202],"computable":[56],"functions":[57,172,205],"(a":[58],"claim":[59],"which":[60,136,161,173],"has":[61],"come":[62],"be":[64],"known":[65],"Church's":[67,102,146],"Thesis);":[68],"and":[69,93,121,186,209],"used":[71],"fact":[73],"solve":[75],"negatively":[76],"some":[77],"classical":[78],"problems":[79],"on":[80],"existence":[82],"algorithms.":[84],"However,":[85],"it":[86,123],"Kleene":[88,198],"who,":[89],"in":[90,94,149,168,221],"his":[91,95,128,154,217],"thesis":[92,218],"subsequent":[96],"attempts":[97],"convince":[99],"himself":[100],"Thesis,":[103],"developed":[104],"general":[106],"behavior":[110],"functions.":[114,145,178],"He":[115],"continued":[116],"develop":[118],"extend":[122],"new":[125],"situations":[126],"throughout":[127],"mathematical":[129],"career.":[130],"Indeed,":[131],"all":[132],"research":[135],"he":[137,162,174],"did":[138],"had":[139,163],"close":[141],"relationship":[142],"Thesis":[147],"arose":[148],"an":[150,213],"accidental":[151],"way.":[152],"investigations":[155],"system":[158],"logic":[160],"invented,":[164],"Church":[165,180],"became":[166,212],"interested":[167],"called":[175],"\u03bb-definable":[177],"Initially,":[179],"knew":[181],"successor":[184],"function":[185,189],"addition":[188],"were":[190],"\u03bb-definable,":[191],"but":[192],"not":[193],"much":[194],"else.":[195],"During":[196],"1932,":[197],"gradually":[199],"showed1":[200],"quite":[207],"extensive;":[208],"these":[210],"results":[211],"important":[214],"part":[215],"1935a":[219],"(completed":[220],"June":[222],"1933).":[224]},"counts_by_year":[{"year":2013,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}