{"id":"https://openalex.org/W2901423989","doi":"https://doi.org/10.1002/malq.201800029","title":"Relations between cardinalities of the finite sequences and the finite subsets of a set","display_name":"Relations between cardinalities of the finite sequences and the finite subsets of a set","publication_year":2018,"publication_date":"2018-11-19","ids":{"openalex":"https://openalex.org/W2901423989","doi":"https://doi.org/10.1002/malq.201800029","mag":"2901423989"},"language":"en","primary_location":{"id":"doi:10.1002/malq.201800029","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201800029","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","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/A5057766682","display_name":"Navin Aksornthong","orcid":null},"institutions":[{"id":"https://openalex.org/I158708052","display_name":"Chulalongkorn University","ror":"https://ror.org/028wp3y58","country_code":"TH","type":"education","lineage":["https://openalex.org/I158708052"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Navin Aksornthong","raw_affiliation_strings":["Department of Mathematics and Computer Science Faculty of Science Chulalongkorn University Payathai Road Patumwan Bangkok 10330 Thailand","Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Payathai Road, Patumwan, Bangkok, 10330 Thailand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science Faculty of Science Chulalongkorn University Payathai Road Patumwan Bangkok 10330 Thailand","institution_ids":["https://openalex.org/I158708052"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Payathai Road, Patumwan, Bangkok, 10330 Thailand","institution_ids":["https://openalex.org/I158708052"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028101911","display_name":"Pimpen Vejjajiva","orcid":"https://orcid.org/0000-0001-8583-2989"},"institutions":[{"id":"https://openalex.org/I158708052","display_name":"Chulalongkorn University","ror":"https://ror.org/028wp3y58","country_code":"TH","type":"education","lineage":["https://openalex.org/I158708052"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Pimpen Vejjajiva","raw_affiliation_strings":["Department of Mathematics and Computer Science Faculty of Science Chulalongkorn University Payathai Road Patumwan Bangkok 10330 Thailand","Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Payathai Road, Patumwan, Bangkok, 10330 Thailand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science Faculty of Science Chulalongkorn University Payathai Road Patumwan Bangkok 10330 Thailand","institution_ids":["https://openalex.org/I158708052"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Payathai Road, Patumwan, Bangkok, 10330 Thailand","institution_ids":["https://openalex.org/I158708052"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5028101911"],"corresponding_institution_ids":["https://openalex.org/I158708052"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.22266416,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"64","issue":"6","first_page":"529","last_page":"534"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9997000098228455,"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":0.9997000098228455,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9898999929428101,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.982200026512146,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/mathematics","display_name":"Mathematics","score":0.8782309889793396},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.8671417236328125},{"id":"https://openalex.org/keywords/dedekind-cut","display_name":"Dedekind cut","score":0.8540918231010437},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.8109681606292725},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.7376757860183716},{"id":"https://openalex.org/keywords/infinite-set","display_name":"Infinite set","score":0.6612015962600708},{"id":"https://openalex.org/keywords/zermelo\u2013fraenkel-set-theory","display_name":"Zermelo\u2013Fraenkel set theory","score":0.6131144165992737},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5643172264099121},{"id":"https://openalex.org/keywords/cardinal-number","display_name":"Cardinal number (linguistics)","score":0.5430554151535034},{"id":"https://openalex.org/keywords/uncountable-set","display_name":"Uncountable set","score":0.5155181884765625},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.4967944920063019},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4727547764778137},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44950070977211},{"id":"https://openalex.org/keywords/urelement","display_name":"Urelement","score":0.4268966317176819},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.34757906198501587},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.13432982563972473},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06320440769195557},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06299197673797607},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04138490557670593}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8782309889793396},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.8671417236328125},{"id":"https://openalex.org/C76449584","wikidata":"https://www.wikidata.org/wiki/Q851333","display_name":"Dedekind cut","level":2,"score":0.8540918231010437},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.8109681606292725},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.7376757860183716},{"id":"https://openalex.org/C199879729","wikidata":"https://www.wikidata.org/wiki/Q205140","display_name":"Infinite set","level":3,"score":0.6612015962600708},{"id":"https://openalex.org/C51460","wikidata":"https://www.wikidata.org/wiki/Q191849","display_name":"Zermelo\u2013Fraenkel set theory","level":5,"score":0.6131144165992737},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5643172264099121},{"id":"https://openalex.org/C2778408900","wikidata":"https://www.wikidata.org/wiki/Q1329258","display_name":"Cardinal number (linguistics)","level":2,"score":0.5430554151535034},{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.5155181884765625},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.4967944920063019},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4727547764778137},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44950070977211},{"id":"https://openalex.org/C78550038","wikidata":"https://www.wikidata.org/wiki/Q1896657","display_name":"Urelement","level":5,"score":0.4268966317176819},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.34757906198501587},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.13432982563972473},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06320440769195557},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06299197673797607},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04138490557670593},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.201800029","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201800029","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4699999988079071,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W328650061","https://openalex.org/W573961896","https://openalex.org/W1608084331","https://openalex.org/W1996087038","https://openalex.org/W2028322461","https://openalex.org/W2071343329","https://openalex.org/W2126219331","https://openalex.org/W2134141694","https://openalex.org/W2222958155"],"related_works":["https://openalex.org/W197851155","https://openalex.org/W1985277111","https://openalex.org/W1991980065","https://openalex.org/W3048792601","https://openalex.org/W1991020681","https://openalex.org/W177504871","https://openalex.org/W4244304300","https://openalex.org/W4293874521","https://openalex.org/W1549623609","https://openalex.org/W2901423989"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"write":[2],"and":[3,13,45,62,92],"for":[4,35,46,64,82,88],"the":[5,8,14,29,78,93],"cardinalities":[6],"of":[7,10,16,20,25,31,80,84],"set":[9,15,22],"finite":[11,17,85],"sequences":[12],"subsets,":[18],"respectively,":[19],"a":[21],"which":[23],"is":[24,96],"cardinality":[26],".":[27,68],"With":[28],"axiom":[30,79],"choice":[32,81],"(":[33],"),":[34],"every":[36,89],"infinite":[37,49,66],"cardinal":[38,50,67,91],"but,":[39],"without":[40],",":[41],"any":[42],"relationship":[43],"between":[44],"an":[47,65],"arbitrary":[48],"cannot":[51,98],"be":[52,99],"proved.":[53],"In":[54],"this":[55],"paper,":[56],"we":[57,72,76],"give":[58],"conditions":[59],"that":[60,95],"make":[61],"comparable":[63],"Among":[69],"our":[70],"results,":[71],"show":[73],"that,":[74],"if":[75],"assume":[77],"sets":[83],"sets,":[86],"then":[87],"Dedekind\u2010infinite":[90,97],"condition":[94],"weakened":[100],"to":[101],"weakly":[102],"Dedekind\u2010infinite.":[103]},"counts_by_year":[{"year":2022,"cited_by_count":3}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
