{"id":"https://openalex.org/W2901729602","doi":"https://doi.org/10.1002/malq.201400079","title":"The gap\u2010two cardinal problem for uncountable languages","display_name":"The gap\u2010two cardinal problem for uncountable languages","publication_year":2018,"publication_date":"2018-11-01","ids":{"openalex":"https://openalex.org/W2901729602","doi":"https://doi.org/10.1002/malq.201400079","mag":"2901729602"},"language":"en","primary_location":{"id":"doi:10.1002/malq.201400079","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201400079","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","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/A5019813301","display_name":"Luis Miguel Villegas Silva","orcid":null},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]},{"id":"https://openalex.org/I200362191","display_name":"Universidad Aut\u00f3noma Metropolitana","ror":"https://ror.org/02kta5139","country_code":"MX","type":"education","lineage":["https://openalex.org/I200362191"]}],"countries":["DE","MX"],"is_corresponding":true,"raw_author_name":"Luis Miguel Villegas Silva","raw_affiliation_strings":["Abteilung f\u00fcr Mathematische Logik Albert\u2010Ludwigs\u2010Universit\u00e4t Freiburg Ernst\u2010Zermelo\u2010Stra\u00dfe 1 79104 Freiburg Germany","Departamento de Matem\u00e1ticas Universidad Aut\u00f3noma Metropolitana Iztapalapa Av. San Rafael Atlixco 186, Col. Vicentina Iztapalapa 09340 D.F. M\u00e9xico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Abteilung f\u00fcr Mathematische Logik Albert\u2010Ludwigs\u2010Universit\u00e4t Freiburg Ernst\u2010Zermelo\u2010Stra\u00dfe 1 79104 Freiburg Germany","institution_ids":["https://openalex.org/I161046081"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas Universidad Aut\u00f3noma Metropolitana Iztapalapa Av. San Rafael Atlixco 186, Col. Vicentina Iztapalapa 09340 D.F. M\u00e9xico","institution_ids":["https://openalex.org/I200362191"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019813301"],"corresponding_institution_ids":["https://openalex.org/I161046081","https://openalex.org/I200362191"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.22676495,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"64","issue":"4-5","first_page":"262","last_page":"285"},"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":0.9986000061035156,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/uncountable-set","display_name":"Uncountable set","score":0.9805545806884766},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7481251955032349},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.5549349784851074},{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.5392277836799622},{"id":"https://openalex.org/keywords/regular-cardinal","display_name":"Regular cardinal","score":0.5232164859771729},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.4945497214794159},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4863760769367218},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.43758222460746765},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33403974771499634},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17999359965324402},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.15132847428321838},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.14101827144622803},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.11060088872909546},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.04676365852355957},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.044724106788635254}],"concepts":[{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.9805545806884766},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7481251955032349},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.5549349784851074},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.5392277836799622},{"id":"https://openalex.org/C89507440","wikidata":"https://www.wikidata.org/wiki/Q1193137","display_name":"Regular cardinal","level":2,"score":0.5232164859771729},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.4945497214794159},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4863760769367218},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.43758222460746765},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33403974771499634},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17999359965324402},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.15132847428321838},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.14101827144622803},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.11060088872909546},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.04676365852355957},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.044724106788635254}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/malq.201400079","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201400079","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","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"},{"id":"pmh:oai:freidok.uni-freiburg.de:270296","is_oa":false,"landing_page_url":"https://freidok.uni-freiburg.de/data/270296","pdf_url":null,"source":{"id":"https://openalex.org/S4306401057","display_name":"FreiDok plus (Universit\u00e4tsbibliothek Freiburg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I161046081","host_organization_name":"University of Freiburg","host_organization_lineage":["https://openalex.org/I161046081"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Logic Quarterly. - 64, 4-5 (2018) , 262-285, ISSN: 1521-3870","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G600271744","display_name":null,"funder_award_id":"140 186412","funder_id":"https://openalex.org/F4320321739","funder_display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda"}],"funders":[{"id":"https://openalex.org/F4320321739","display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","ror":"https://ror.org/059ex5q34"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W568910110","https://openalex.org/W2122092051","https://openalex.org/W2231257830","https://openalex.org/W2575229636","https://openalex.org/W4234245490"],"related_works":["https://openalex.org/W4289676933","https://openalex.org/W2950296149","https://openalex.org/W2885719937","https://openalex.org/W4297981628","https://openalex.org/W2952331208","https://openalex.org/W4298219619","https://openalex.org/W2097355897","https://openalex.org/W2167408243","https://openalex.org/W2567038806","https://openalex.org/W2557290701"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper":[3],"we":[4,51],"prove":[5],"some":[6],"cases":[7],"of":[8,20],"the":[9,18],"gap\u20102":[10],"cardinal":[11],"transfer":[12],"theorem":[13],"for":[14],"uncountable":[15,23],"languages":[16],"assuming":[17],"axiom":[19],"constructibility.":[21],"Consider":[22],"cardinals":[24],",":[25,41,47,50,57],"with":[26,33,42],"\u03bb":[27],"regular,":[28],"a":[29],"first":[30],"order":[31],"language":[32],"at":[34],"least":[35],"one":[36],"unary":[37],"predicate":[38],"symbol":[39],"U":[40],".":[43,59],"Given":[44],"an":[45,53],"\u2010structure":[46,54],"where":[48],"and":[49,58],"find":[52],"such":[55],"that":[56]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}