{"id":"https://openalex.org/W2138217322","doi":"https://doi.org/10.2307/2586807","title":"A set with barely degree","display_name":"A set with barely degree","publication_year":1999,"publication_date":"1999-12-01","ids":{"openalex":"https://openalex.org/W2138217322","doi":"https://doi.org/10.2307/2586807","mag":"2138217322"},"language":"en","primary_location":{"id":"doi:10.2307/2586807","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586807","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/A5110868906","display_name":"Rod Downey","orcid":null},"institutions":[{"id":"https://openalex.org/I41156924","display_name":"Victoria University of Wellington","ror":"https://ror.org/0040r6f76","country_code":"NZ","type":"education","lineage":["https://openalex.org/I41156924"]},{"id":"https://openalex.org/I71270174","display_name":"Victoria University","ror":"https://ror.org/04j757h98","country_code":"AU","type":"education","lineage":["https://openalex.org/I71270174"]}],"countries":["AU","NZ"],"is_corresponding":false,"raw_author_name":"Rod Downey","raw_affiliation_strings":["School of Mathematical and Computer Sciences, Victoria University, Po Box 600, Wellington, New Zealand, E-mail:","School of Mathematical and Computer Sciences, Victoria University, Po Box 600, Wellington, New Zealand, E-mail: rod.downey@vuw.ac.nz"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical and Computer Sciences, Victoria University, Po Box 600, Wellington, New Zealand, E-mail:","institution_ids":["https://openalex.org/I41156924"]},{"raw_affiliation_string":"School of Mathematical and Computer Sciences, Victoria University, Po Box 600, Wellington, New Zealand, E-mail: rod.downey@vuw.ac.nz","institution_ids":["https://openalex.org/I71270174"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037735865","display_name":"Geoffrey Laforte","orcid":null},"institutions":[{"id":"https://openalex.org/I1335578998","display_name":"Florida Institute for Human and Machine Cognition","ror":"https://ror.org/02napvw46","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1335578998"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Geoffrey Laforte","raw_affiliation_strings":["Institute For Human and Machine Cognition, 11000 University Parkway, Pensacola. FL 32514, USA, E-mail:","Institute For Human and Machine Cognition, 11000 University Parkway, Pensacola. FL 32514, USA, E-mail: glaforte@ai.uwf.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute For Human and Machine Cognition, 11000 University Parkway, Pensacola. FL 32514, USA, E-mail:","institution_ids":["https://openalex.org/I1335578998"]},{"raw_affiliation_string":"Institute For Human and Machine Cognition, 11000 University Parkway, Pensacola. FL 32514, USA, E-mail: glaforte@ai.uwf.edu","institution_ids":["https://openalex.org/I1335578998"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032435178","display_name":"Steffen Lempp","orcid":"https://orcid.org/0000-0002-2958-4017"},"institutions":[{"id":"https://openalex.org/I1304256225","display_name":"University of Wisconsin System","ror":"https://ror.org/03ydkyb10","country_code":"US","type":"education","lineage":["https://openalex.org/I1304256225"]},{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Steffen Lempp","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706-1388, USA, E-mail:","Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706-1388, USA, E-mail: lempp@math.wisc.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706-1388, USA, E-mail:","institution_ids":["https://openalex.org/I1304256225","https://openalex.org/I135310074"]},{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706-1388, USA, E-mail: lempp@math.wisc.edu","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23495951,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"64","issue":"4","first_page":"1700","last_page":"1718"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9713000059127808,"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":0.9514999985694885,"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":0.8760209679603577},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6941736936569214},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6795428395271301},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.6760338544845581},{"id":"https://openalex.org/keywords/recursively-enumerable-language","display_name":"Recursively enumerable language","score":0.5824411511421204},{"id":"https://openalex.org/keywords/maximal-set","display_name":"Maximal set","score":0.41876375675201416},{"id":"https://openalex.org/keywords/recursively-enumerable-set","display_name":"Recursively enumerable set","score":0.41522789001464844},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.368344247341156},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25703850388526917},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.07329964637756348},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.026384085416793823}],"concepts":[{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.8760209679603577},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6941736936569214},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6795428395271301},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.6760338544845581},{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.5824411511421204},{"id":"https://openalex.org/C188521023","wikidata":"https://www.wikidata.org/wiki/Q6795644","display_name":"Maximal set","level":3,"score":0.41876375675201416},{"id":"https://openalex.org/C52703633","wikidata":"https://www.wikidata.org/wiki/Q676835","display_name":"Recursively enumerable set","level":3,"score":0.41522789001464844},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.368344247341156},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25703850388526917},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.07329964637756348},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.026384085416793823},{"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:10.2307/2586807","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586807","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1972685794","https://openalex.org/W2016891068","https://openalex.org/W2056414301","https://openalex.org/W4232277851"],"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/W2000487993","https://openalex.org/W1980641386","https://openalex.org/W4249600134"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"construct":[2],"a":[3],"degree":[4],"which":[5],"fails":[6],"to":[7],"be":[8],"computably":[9,13],"enumerable":[10,14],"in":[11],"any":[12],"set":[15],"strictly":[16],"below":[17],".":[18]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}