{"id":"https://openalex.org/W2072032541","doi":"https://doi.org/10.2307/2695113","title":"A \u0394<sub>2</sub><sup>0</sup> set with no infinite low subset in either it or its complement","display_name":"A \u0394<sub>2</sub><sup>0</sup> set with no infinite low subset in either it or its complement","publication_year":2001,"publication_date":"2001-09-01","ids":{"openalex":"https://openalex.org/W2072032541","doi":"https://doi.org/10.2307/2695113","mag":"2072032541"},"language":"en","primary_location":{"id":"doi:10.2307/2695113","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2695113","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"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Rod Downey","raw_affiliation_strings":["School of Mathematical and Computing Sciences, Victoria University, P.O. Box 600, Wellington, New Zealand, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical and Computing Sciences, Victoria University, P.O. Box 600, Wellington, New Zealand, E-mail:","institution_ids":["https://openalex.org/I41156924"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015485533","display_name":"Denis R. Hirschfeldt","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"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"Denis R. Hirschfeldt","raw_affiliation_strings":["School of Mathematical and Computing Sciences, Victoria University, P.O. Box 600, Wellington, New Zealand, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical and Computing Sciences, Victoria University, P.O. Box 600, Wellington, New Zealand, E-mail:","institution_ids":["https://openalex.org/I41156924"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032435178","display_name":"Steffen Lempp","orcid":"https://orcid.org/0000-0002-2958-4017"},"institutions":[{"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, Madison, WI 53706-1388, USA, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin, Madison, WI 53706-1388, USA, E-mail:","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072805118","display_name":"Reed Solomon","orcid":"https://orcid.org/0000-0001-7574-204X"},"institutions":[{"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":"Reed Solomon","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin, Madison, WI 53706-1388, USA, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin, Madison, WI 53706-1388, USA, E-mail:","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5015485533"],"corresponding_institution_ids":["https://openalex.org/I41156924"],"apc_list":null,"apc_paid":null,"fwci":1.4372,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.80101225,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"66","issue":"3","first_page":"1371","last_page":"1381"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9955000281333923,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9955000281333923,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9703999757766724,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9106000065803528,"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/complement","display_name":"Complement (music)","score":0.8767058849334717},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.7201715111732483},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.698082447052002},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48014017939567566},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4469708502292633},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4196658432483673},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34422019124031067},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.06382369995117188},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.06264689564704895}],"concepts":[{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.8767058849334717},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.7201715111732483},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.698082447052002},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48014017939567566},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4469708502292633},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4196658432483673},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34422019124031067},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.06382369995117188},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.06264689564704895},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2695113","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2695113","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":3,"referenced_works":["https://openalex.org/W1556453281","https://openalex.org/W2148962283","https://openalex.org/W4232277851"],"related_works":["https://openalex.org/W2366107444","https://openalex.org/W4388145910","https://openalex.org/W2381570729","https://openalex.org/W1976205134","https://openalex.org/W4248336175","https://openalex.org/W2031260042","https://openalex.org/W2391445434","https://openalex.org/W3009369890","https://openalex.org/W4312490297","https://openalex.org/W2062212388"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"construct":[2],"the":[3,6,22,25],"set":[4],"of":[5,11,24,31,33,45],"title,":[7],"answering":[8],"a":[9,48],"question":[10],"Cholak,":[12],"Jockusch.":[13],"and":[14,17,28],"Slaman":[15],"[1],":[16],"discuss":[18],"its":[19],"connections":[20],"with":[21],"study":[23],"proof-theoretic":[26],"strength":[27],"effective":[29],"content":[30],"versions":[32],"Ramsey's":[34],"Theorem.":[35],"In":[36],"particular,":[37],"our":[38],"result":[39],"implies":[40],"that":[41],"every":[42],"\u03c9":[43],"-model":[44],"must":[46],"contain":[47],"nonlow":[49],"set.":[50]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"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":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
