{"id":"https://openalex.org/W2102454352","doi":"https://doi.org/10.2307/2271101","title":"A note on degrees of subsets<sup>1</sup>","display_name":"A note on degrees of subsets<sup>1</sup>","publication_year":1969,"publication_date":"1969-07-25","ids":{"openalex":"https://openalex.org/W2102454352","doi":"https://doi.org/10.2307/2271101","mag":"2102454352"},"language":"en","primary_location":{"id":"doi:10.2307/2271101","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271101","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/A5023422267","display_name":"Robert I. Soare","orcid":null},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Robert I. Soare","raw_affiliation_strings":["University of Illinois at Chicago Circle"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois at Chicago Circle","institution_ids":["https://openalex.org/I39422238"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023422267"],"corresponding_institution_ids":["https://openalex.org/I39422238"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.26386933,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"34","issue":"2","first_page":"256","last_page":"256"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9950000047683716,"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/T11567","display_name":"semigroups and automata theory","score":0.968999981880188,"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/degree","display_name":"Degree (music)","score":0.8405433297157288},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7487843036651611},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.7356905937194824},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6577745676040649},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6420139074325562},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4833804965019226},{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.4240572154521942},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13757184147834778},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06075158715248108}],"concepts":[{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.8405433297157288},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7487843036651611},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.7356905937194824},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6577745676040649},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6420139074325562},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4833804965019226},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.4240572154521942},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13757184147834778},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06075158715248108},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2271101","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271101","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W2058683290","https://openalex.org/W2530006810","https://openalex.org/W2905135108","https://openalex.org/W6665244162"],"related_works":["https://openalex.org/W3161230432","https://openalex.org/W1487201914","https://openalex.org/W4367190712","https://openalex.org/W280458463","https://openalex.org/W1170131723","https://openalex.org/W4301429470","https://openalex.org/W2168900540","https://openalex.org/W2125310826","https://openalex.org/W2586471321","https://openalex.org/W2007089758"],"abstract_inverted_index":{"In":[0],"[2]":[1],"we":[2],"constructed":[3],"an":[4],"infinite":[5,58],"set":[6,59],"of":[7,13,29,36,65],"natural":[8,41],"numbers":[9],"containing":[10,32],"no":[11,33],"subset":[12,35,64],"higher":[14,67],"(Turing)":[15],"degree.":[16,70],"Since":[17],"it":[18,39],"is":[19,40,52],"well":[20],"known":[21],"that":[22,44,56],"there":[23],"are":[24],"nonrecursive":[25,34,63],"sets":[26,28],"(e.g.":[27],"minimal":[30],"degree)":[31],"lower":[37,69],"degree,":[38],"to":[42],"suppose":[43],"these":[45],"arguments":[46],"may":[47],"be":[48],"combined,":[49],"but":[50],"this":[51],"false.":[53],"We":[54],"prove":[55],"every":[57],"must":[60],"contain":[61],"a":[62],"either":[66],"or":[68]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
