{"id":"https://openalex.org/W2102988122","doi":"https://doi.org/10.2178/jsl/1102022208","title":"Minimal complements for degrees below 0\u2032","display_name":"Minimal complements for degrees below 0\u2032","publication_year":2004,"publication_date":"2004-12-01","ids":{"openalex":"https://openalex.org/W2102988122","doi":"https://doi.org/10.2178/jsl/1102022208","mag":"2102988122"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1102022208","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1102022208","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/A5057895970","display_name":"Andrew D. Lewis","orcid":"https://orcid.org/0000-0001-7342-4275"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Andrew Lewis","raw_affiliation_strings":["Department of Pure Mathematics, School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK, E-mail:","Department of Pure Mathematics, School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK, E-mail: thelewisboy@hotmail.com"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK, E-mail:","institution_ids":["https://openalex.org/I130828816"]},{"raw_affiliation_string":"Department of Pure Mathematics, School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK, E-mail: thelewisboy@hotmail.com","institution_ids":["https://openalex.org/I130828816"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057895970"],"corresponding_institution_ids":["https://openalex.org/I130828816"],"apc_list":null,"apc_paid":null,"fwci":2.0518,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.86894213,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"69","issue":"4","first_page":"937","last_page":"966"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T11567","display_name":"semigroups and automata theory","score":0.9962000250816345,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9927999973297119,"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":0.7057781219482422},{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.6325696706771851},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5909410715103149},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4567517042160034},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37272951006889343},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3152207136154175},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10884252190589905},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.08413386344909668}],"concepts":[{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.7057781219482422},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.6325696706771851},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5909410715103149},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4567517042160034},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37272951006889343},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3152207136154175},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10884252190589905},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.08413386344909668},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1102022208","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1102022208","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/1102022208","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1102022208","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":20,"referenced_works":["https://openalex.org/W623765668","https://openalex.org/W1449003082","https://openalex.org/W1983321159","https://openalex.org/W2039241442","https://openalex.org/W2042499838","https://openalex.org/W2042722323","https://openalex.org/W2055051664","https://openalex.org/W2056414301","https://openalex.org/W2068756392","https://openalex.org/W2073364886","https://openalex.org/W2105112555","https://openalex.org/W2113021297","https://openalex.org/W2131652429","https://openalex.org/W2144999713","https://openalex.org/W2145265838","https://openalex.org/W2167930025","https://openalex.org/W4232277851","https://openalex.org/W4241435086","https://openalex.org/W6660270338","https://openalex.org/W6811663084"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"Abstract.":[0],"It":[1],"is":[2,15],"shown":[3],"that":[4,23],"for":[5],"every":[6],"(Turing)":[7],"degree":[8,18],"0":[9],"&lt;":[10,12,20],"a":[11,16,24,31],"0\u2032":[13,21,28],"there":[14],"minimal":[17],"m":[19,26,33],"such":[22],"\u2228":[25],"=":[27,34],"(and":[29],"therefore":[30],"\u2227":[32],"0).":[35]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
