{"id":"https://openalex.org/W2080194306","doi":"https://doi.org/10.2307/2271441","title":"Recursion theory and formal deducibility","display_name":"Recursion theory and formal deducibility","publication_year":1970,"publication_date":"1970-12-01","ids":{"openalex":"https://openalex.org/W2080194306","doi":"https://doi.org/10.2307/2271441","mag":"2080194306"},"language":"en","primary_location":{"id":"doi:10.2307/2271441","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271441","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/A5034562840","display_name":"E. M. Kleinberg","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"E. M. Kleinberg","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, Massachusetts","Massachusetts Institute of Technology, Cambridge, Massachusetts#TAB#"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, Massachusetts","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, Massachusetts#TAB#","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5034562840"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23259334,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"35","issue":"4","first_page":"556","last_page":"558"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9911999702453613,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9911999702453613,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9853000044822693,"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":0.9850999712944031,"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/enumeration","display_name":"Enumeration","score":0.8154882192611694},{"id":"https://openalex.org/keywords/recursively-enumerable-language","display_name":"Recursively enumerable language","score":0.7022591233253479},{"id":"https://openalex.org/keywords/sentence","display_name":"Sentence","score":0.6507308483123779},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.6314525008201599},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.620068371295929},{"id":"https://openalex.org/keywords/first-order-logic","display_name":"First-order logic","score":0.5958889722824097},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5764614343643188},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4961317479610443},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47520408034324646},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.47292572259902954},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.47078412771224976},{"id":"https://openalex.org/keywords/sort","display_name":"sort","score":0.4554885923862457},{"id":"https://openalex.org/keywords/computability-theory","display_name":"Computability theory","score":0.45485854148864746},{"id":"https://openalex.org/keywords/order-type","display_name":"Order type","score":0.42166370153427124},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.2702332139015198},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25015854835510254},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2136537730693817},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12015771865844727}],"concepts":[{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.8154882192611694},{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.7022591233253479},{"id":"https://openalex.org/C2777530160","wikidata":"https://www.wikidata.org/wiki/Q41796","display_name":"Sentence","level":2,"score":0.6507308483123779},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.6314525008201599},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.620068371295929},{"id":"https://openalex.org/C100481476","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"First-order logic","level":2,"score":0.5958889722824097},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5764614343643188},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4961317479610443},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47520408034324646},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47292572259902954},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47078412771224976},{"id":"https://openalex.org/C88548561","wikidata":"https://www.wikidata.org/wiki/Q347599","display_name":"sort","level":2,"score":0.4554885923862457},{"id":"https://openalex.org/C111142201","wikidata":"https://www.wikidata.org/wiki/Q818930","display_name":"Computability theory","level":2,"score":0.45485854148864746},{"id":"https://openalex.org/C138890893","wikidata":"https://www.wikidata.org/wiki/Q620006","display_name":"Order type","level":2,"score":0.42166370153427124},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2702332139015198},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25015854835510254},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2136537730693817},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12015771865844727},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2271441","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271441","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/1183737376","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183737376","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4388310202","https://openalex.org/W2310420552","https://openalex.org/W2133902039","https://openalex.org/W1589207578","https://openalex.org/W2936847277","https://openalex.org/W167110062","https://openalex.org/W2001962035","https://openalex.org/W4247035339","https://openalex.org/W2467957161","https://openalex.org/W2080194306"],"abstract_inverted_index":{"The":[0],"enumeration,":[1,19],"given":[2,20],"a":[3,21,52,105],"first-order":[4,14,59],"sentence":[5,75],",":[6,25,33,66,76],"of":[7,26,38,55,58,83,100,108],"all":[8,87],"sentences":[9,57,88],"deducible":[10,89],"from":[11,90],"in":[12],"the":[13,18,27,56,70,74,81,95,97,109],"predicate":[15],"calculus,":[16],"and":[17],"non-negative":[22],"integer":[23],"n":[24,32,65,68,79],"recursively":[28],"enumerable":[29],"set":[30,82],"W":[31,78],"are":[34,42],"two":[35],"well-known":[36],"examples":[37],"effective":[39],"processes.":[40],"But":[41],"these":[43],"processes":[44],"really":[45],"distinct?":[46],"Indeed,":[47],"might":[48],"there":[49],"not":[50],"exist":[51],"G\u00f6del":[53],"numbering":[54],"logic":[60],"such":[61],"that":[62],"for":[63],"each":[64],"if":[67],"is":[69,80],"number":[71],"assigned":[72,85],"to":[73,86],"then":[77],"numbers":[84],"?":[91],"If":[92],"this":[93],"were":[94],"case,":[96],"first":[98],"sort":[99],"enumeration":[101],"would":[102],"just":[103],"be":[104],"particular":[106],"instance":[107],"second.":[110]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
