{"id":"https://openalex.org/W2010228910","doi":"https://doi.org/10.2178/jsl/1140641161","title":"Converse dual cardinals","display_name":"Converse dual cardinals","publication_year":2006,"publication_date":"2006-03-01","ids":{"openalex":"https://openalex.org/W2010228910","doi":"https://doi.org/10.2178/jsl/1140641161","mag":"2010228910"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1140641161","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1140641161","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/A5070977261","display_name":"J\u00f6rg Brendle","orcid":"https://orcid.org/0000-0001-8120-2883"},"institutions":[{"id":"https://openalex.org/I65837984","display_name":"Kobe University","ror":"https://ror.org/03tgsfw79","country_code":"JP","type":"education","lineage":["https://openalex.org/I65837984"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"J\u00f6rg Brendle","raw_affiliation_strings":["The Graduate School of Science and Technology, Kobe University, Rokko-Dai 1-1, Nada-Ku, Kobe 657-8501, Japan. E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Graduate School of Science and Technology, Kobe University, Rokko-Dai 1-1, Nada-Ku, Kobe 657-8501, Japan. E-mail:","institution_ids":["https://openalex.org/I65837984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022127133","display_name":"Shuguo Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuguo Zhang","raw_affiliation_strings":["Mathematical College, Sichuan University Chengdu, Sichuan 610064, P. R. China. E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical College, Sichuan University Chengdu, Sichuan 610064, P. R. China. E-mail:","institution_ids":["https://openalex.org/I24185976"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3892,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.56072051,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"71","issue":"1","first_page":"22","last_page":"34"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9930999875068665,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9879999756813049,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/converse","display_name":"Converse","score":0.9115322828292847},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7151138186454773},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5949578881263733},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.57060706615448},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5486583709716797},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4506084620952606},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4171847701072693},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3675549030303955},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.1023516058921814},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0703531801700592},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.05453971028327942}],"concepts":[{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.9115322828292847},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7151138186454773},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5949578881263733},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.57060706615448},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5486583709716797},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4506084620952606},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4171847701072693},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3675549030303955},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.1023516058921814},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0703531801700592},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.05453971028327942}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1140641161","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1140641161","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/1140641161","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1140641161","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":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.41999998688697815}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W176101492","https://openalex.org/W881879546","https://openalex.org/W1997761346","https://openalex.org/W1998711221","https://openalex.org/W2030502591","https://openalex.org/W2084193616","https://openalex.org/W2090388769","https://openalex.org/W2134581608","https://openalex.org/W2135756492","https://openalex.org/W2503186209","https://openalex.org/W4213019076","https://openalex.org/W6607208279"],"related_works":["https://openalex.org/W2387449261","https://openalex.org/W2418518962","https://openalex.org/W2963377682","https://openalex.org/W2043159103","https://openalex.org/W2391769344","https://openalex.org/W4297790016","https://openalex.org/W2359260952","https://openalex.org/W186811874","https://openalex.org/W2074733683","https://openalex.org/W2007089758"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"investigate":[2],"the":[3,11,42,54,67],"set":[4],"(":[5],"\u03c9":[6,57],")":[7],"of":[8,10,27,44,47,62,66],"partitions":[9],"natural":[12],"numbers":[13],"ordered":[14],"by":[15,22],"\u2264*":[16,19],"where":[17],"A":[18,28],"B":[20,36],"if":[21],"gluing":[23],"finitely":[24],"many":[25],"blocks":[26],"we":[29,40],"can":[30],"get":[31],"a":[32,45],"partition":[33],"coarser":[34],"than":[35],".":[37],"In":[38],"particular,":[39],"determine":[41],"values":[43],"number":[46],"cardinals":[48],"which":[49],"are":[50],"naturally":[51],"associated":[52],"with":[53],"structure":[55],"((":[56],"),":[58],"\u2265*),":[59],"in":[60],"terms":[61],"classical":[63],"cardinal":[64],"invariants":[65],"continuum.":[68]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2025-10-10T00:00:00"}