{"id":"https://openalex.org/W2051601785","doi":"https://doi.org/10.2307/2269807","title":"A minimal pair of recursively enumerable degrees","display_name":"A minimal pair of recursively enumerable degrees","publication_year":1966,"publication_date":"1966-06-01","ids":{"openalex":"https://openalex.org/W2051601785","doi":"https://doi.org/10.2307/2269807","mag":"2051601785"},"language":"en","primary_location":{"id":"doi:10.2307/2269807","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2269807","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/A5112795614","display_name":"C. E. M. Yates","orcid":null},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"C. E. M. Yates","raw_affiliation_strings":["Cornell University, Institute for Advanced Study"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cornell University, Institute for Advanced Study","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112795614"],"corresponding_institution_ids":["https://openalex.org/I205783295"],"apc_list":null,"apc_paid":null,"fwci":1.5476,"has_fulltext":false,"cited_by_count":144,"citation_normalized_percentile":{"value":0.83896696,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"31","issue":"2","first_page":"159","last_page":"168"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":1.0,"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":1.0,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/recursively-enumerable-language","display_name":"Recursively enumerable language","score":0.9718791246414185},{"id":"https://openalex.org/keywords/recursively-enumerable-set","display_name":"Recursively enumerable set","score":0.8120889663696289},{"id":"https://openalex.org/keywords/semilattice","display_name":"Semilattice","score":0.6652880311012268},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6435378193855286},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5661098957061768},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5648808479309082},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5340285301208496},{"id":"https://openalex.org/keywords/existential-quantification","display_name":"Existential quantification","score":0.5091878771781921},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5032228827476501},{"id":"https://openalex.org/keywords/maximal-set","display_name":"Maximal set","score":0.4616277515888214},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18735402822494507},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06418272852897644},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.044165968894958496}],"concepts":[{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.9718791246414185},{"id":"https://openalex.org/C52703633","wikidata":"https://www.wikidata.org/wiki/Q676835","display_name":"Recursively enumerable set","level":3,"score":0.8120889663696289},{"id":"https://openalex.org/C132170107","wikidata":"https://www.wikidata.org/wiki/Q834585","display_name":"Semilattice","level":3,"score":0.6652880311012268},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6435378193855286},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5661098957061768},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5648808479309082},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5340285301208496},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.5091878771781921},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5032228827476501},{"id":"https://openalex.org/C188521023","wikidata":"https://www.wikidata.org/wiki/Q6795644","display_name":"Maximal set","level":3,"score":0.4616277515888214},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18735402822494507},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06418272852897644},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.044165968894958496},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2269807","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2269807","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/1183735415","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183735415","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":7,"referenced_works":["https://openalex.org/W111095393","https://openalex.org/W1483568252","https://openalex.org/W2015965037","https://openalex.org/W2037416374","https://openalex.org/W2045033949","https://openalex.org/W2055051664","https://openalex.org/W4241435086"],"related_works":["https://openalex.org/W2037833610","https://openalex.org/W2089792255","https://openalex.org/W2135152748","https://openalex.org/W2069987267","https://openalex.org/W1973052363","https://openalex.org/W1972481159","https://openalex.org/W2112189052","https://openalex.org/W1980641386","https://openalex.org/W2051601785","https://openalex.org/W3135018072"],"abstract_inverted_index":{"Our":[0],"principal":[1],"result":[2],"is":[3,22,61],"that":[4,37,53,81],"there":[5,42],"exist":[6],"two":[7],"incomparable":[8],"recursively":[9,45,57],"enumerable":[10,46,58],"degrees":[11,21],"whose":[12],"greatest":[13,64],"lower":[14,65,106],"bound":[15,66],"in":[16,91],"the":[17,39,63,75],"upper":[18],"semilattice":[19],"of":[20,67,74,105],"0":[23,50,62],".":[24,71],"This":[25],"was":[26],"conjectured":[27],"by":[28],"Sacks":[29],"[5].":[30],"As":[31],"a":[32,44,48,68,79,93],"secondary":[33],"result,":[34],"we":[35,82],"prove":[36],"on":[38],"other":[40],"hand":[41],"exists":[43],"degree":[47,59],"&lt;":[49],"(1)":[51],"such":[52],"for":[54],"no":[55],"non-zero":[56],"b":[60,70],"and":[69],"The":[72],"proof":[73],"main":[76],"theorem":[77],"involves":[78],"method":[80],"have":[83],"developed":[84],"elsewhere":[85],"[8]":[86],"to":[87],"deal":[88],"with":[89,101],"situations":[90],"which":[92],"partial":[94],"recursive":[95],"functional":[96],"may":[97],"interfere":[98],"infinitely":[99],"often":[100],"an":[102],"opposed":[103],"requirement":[104],"priority.":[107]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
