{"id":"https://openalex.org/W2015376829","doi":"https://doi.org/10.2307/2266510","title":"Definability and decision problems in arithmetic","display_name":"Definability and decision problems in arithmetic","publication_year":1949,"publication_date":"1949-06-23","ids":{"openalex":"https://openalex.org/W2015376829","doi":"https://doi.org/10.2307/2266510","mag":"2015376829"},"language":"en","primary_location":{"id":"doi:10.2307/2266510","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2266510","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/A5112046050","display_name":"Julia Robinson","orcid":null},"institutions":[{"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":true,"raw_author_name":"Julia Robinson","raw_affiliation_strings":["University of California"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California","institution_ids":["https://openalex.org/I2803209242"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112046050"],"corresponding_institution_ids":["https://openalex.org/I2803209242"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":14.2182,"has_fulltext":false,"cited_by_count":326,"citation_normalized_percentile":{"value":0.99380165,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"14","issue":"2","first_page":"98","last_page":"114"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9968000054359436,"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":0.9968000054359436,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.963699996471405,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9596999883651733,"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/unary-operation","display_name":"Unary operation","score":0.9045039415359497},{"id":"https://openalex.org/keywords/successor-cardinal","display_name":"Successor cardinal","score":0.8722326159477234},{"id":"https://openalex.org/keywords/arithmetic-function","display_name":"Arithmetic function","score":0.8151465654373169},{"id":"https://openalex.org/keywords/divisibility-rule","display_name":"Divisibility rule","score":0.7996094226837158},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7935070395469666},{"id":"https://openalex.org/keywords/rational-number","display_name":"Rational number","score":0.6821712851524353},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.6667439341545105},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.6628636121749878},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4463111162185669},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33369892835617065},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2729291617870331},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.26814714074134827}],"concepts":[{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.9045039415359497},{"id":"https://openalex.org/C75306776","wikidata":"https://www.wikidata.org/wiki/Q7632662","display_name":"Successor cardinal","level":2,"score":0.8722326159477234},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.8151465654373169},{"id":"https://openalex.org/C9991821","wikidata":"https://www.wikidata.org/wiki/Q858520","display_name":"Divisibility rule","level":2,"score":0.7996094226837158},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7935070395469666},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.6821712851524353},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6667439341545105},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.6628636121749878},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4463111162185669},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33369892835617065},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2729291617870331},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26814714074134827},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2266510","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2266510","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/1183730618","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183730618","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":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7900000214576721}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W203825433","https://openalex.org/W1975810242","https://openalex.org/W2064811181","https://openalex.org/W2085098223","https://openalex.org/W2114804254","https://openalex.org/W2323777246","https://openalex.org/W2403653109","https://openalex.org/W4245597824","https://openalex.org/W4256369010"],"related_works":["https://openalex.org/W2473542051","https://openalex.org/W3123320268","https://openalex.org/W2994519609","https://openalex.org/W2726593096","https://openalex.org/W2054269721","https://openalex.org/W4312621537","https://openalex.org/W2321536184","https://openalex.org/W1543190560","https://openalex.org/W2521758630","https://openalex.org/W4287960381"],"abstract_inverted_index":{"In":[0,37],"this":[1],"paper,":[2],"we":[3,40],"are":[4],"concerned":[5],"with":[6],"the":[7,56,80],"arithmetical":[8],"definability":[9],"of":[10,13,19,33,44,53,59,77,82],"certain":[11],"notions":[12],"integers":[14,46],"and":[15,55,69,79],"rationals":[16],"in":[17,51,75],"terms":[18,52,76],"other":[20],"notions.":[21],"The":[22],"results":[23],"derived":[24],"will":[25],"be":[26,48,72],"applied":[27],"to":[28],"obtain":[29],"a":[30],"negative":[31],"solution":[32],"corresponding":[34],"decision":[35],"problems.":[36],"Section":[38],"1,":[39],"show":[41],"that":[42,66],"addition":[43,68],"positive":[45],"can":[47,71],"defined":[49,73],"arithmetically":[50,74],"multiplication":[54,70],"unary":[57],"operation":[58],"successorS(whereSa=a+":[60],"1).":[61],"Also,":[62],"it":[63],"is":[64],"shown":[65],"both":[67],"successor":[78],"relation":[81],"divisibility":[83],"|":[84],"(wherex|ymeansxdividesy).":[85]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":34},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":16},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":7}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
