{"id":"https://openalex.org/W1504378551","doi":"https://doi.org/10.2307/2273517","title":"On the compactness of \u2135<sub>1</sub> and \u2135<sub>2</sub>","display_name":"On the compactness of \u2135<sub>1</sub> and \u2135<sub>2</sub>","publication_year":1978,"publication_date":"1978-09-01","ids":{"openalex":"https://openalex.org/W1504378551","doi":"https://doi.org/10.2307/2273517","mag":"1504378551"},"language":"en","primary_location":{"id":"doi:10.2307/2273517","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273517","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/A5056963712","display_name":"Carlos Augusto Di Prisco","orcid":null},"institutions":[{"id":"https://openalex.org/I191242182","display_name":"Instituto Venezolano de Investigaciones Cient\u00edficas","ror":"https://ror.org/02ntheh91","country_code":"VE","type":"facility","lineage":["https://openalex.org/I191242182"]}],"countries":["VE"],"is_corresponding":true,"raw_author_name":"C. A. di Prisco","raw_affiliation_strings":["Instttuto Venezolano de Investigaciones Cient\u00edficas, Caracas, Venezuela"],"affiliations":[{"raw_affiliation_string":"Instttuto Venezolano de Investigaciones Cient\u00edficas, Caracas, Venezuela","institution_ids":["https://openalex.org/I191242182"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054159138","display_name":"Jim Henle","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Henle","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA 02139"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA 02139","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056963712"],"corresponding_institution_ids":["https://openalex.org/I191242182"],"apc_list":null,"apc_paid":null,"fwci":0.6819,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.60896686,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"43","issue":"3","first_page":"394","last_page":"401"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9921000003814697,"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/T12137","display_name":"Economic theories and models","score":0.968500018119812,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.8216005563735962},{"id":"https://openalex.org/keywords/uncountable-set","display_name":"Uncountable set","score":0.716019868850708},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5897052884101868},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5048394799232483},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.4487789571285248},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.4272632300853729},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4039674997329712},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4024999141693115},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28356900811195374},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.07328233122825623}],"concepts":[{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.8216005563735962},{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.716019868850708},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5897052884101868},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5048394799232483},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.4487789571285248},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.4272632300853729},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4039674997329712},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4024999141693115},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28356900811195374},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.07328233122825623},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2273517","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273517","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":[{"score":0.5799999833106995,"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W2066172220","https://openalex.org/W2074199159","https://openalex.org/W2554842236"],"related_works":["https://openalex.org/W2100222222","https://openalex.org/W1982069151","https://openalex.org/W2256572025","https://openalex.org/W4303646992","https://openalex.org/W2952146172","https://openalex.org/W4300882518","https://openalex.org/W2018852434","https://openalex.org/W2068604232","https://openalex.org/W2092513686","https://openalex.org/W2027425357"],"abstract_inverted_index":{"In":[0,187,215],"recent":[1,89],"years,":[2],"the":[3,13,18,75,125,179,203,223,228,238],"Axiom":[4],"of":[5,17,43,91,181],"Determinateness":[6],"(AD)":[7],"has":[8,59],"yielded":[9],"numerous":[10],"results":[11,25],"concerning":[12,48],"size":[14],"and":[15,33,46,69,141,200,236],"properties":[16],"first":[19],"\u03c9-many":[20],"uncountable":[21],"cardinals.":[22],"Briefly,":[23],"these":[24],"began":[26],"with":[27,41],"Solovay's":[28],"discovery":[29],"that":[30,56,74,95,109,142,146,192,207,227,237,245],"\u2135":[31,34,57,61,76,96,99,112,119,147,167,193,196,208,211,246,249],"1":[32,64,97,113,148,168,194],"2":[35,62,100,130,197,209,247],"are":[36,78,233],"measurable":[37],"[8],":[38],"[3],":[39,53],"continued":[40],"theorems":[42],"Solovay,":[44],"Martin,":[45],"Kunen":[47],"infinite-exponent":[49],"partition":[50],"relations":[51],"[6],":[52],"Martin's":[54],"proof":[55,73],"n":[58,66,77],"confinality":[60],"for":[63,106,117,153],"&lt;":[65,67,120,156],"\u03c9,":[68],"very":[70,88],"recently,":[71],"Kleinberg's":[72],"Jonsson":[79],"cardinals":[80],"[4].":[81],"This":[82,175],"paper":[83,176],"was":[84,104],"inspired":[85],"by":[86,225],"a":[87,136,220],"result":[90],"Martin":[92,182],"from":[93],"AD":[94,110,143,173],"is":[98,114,124,150,169,195,210,248],"-super":[101,198],"compact.":[102,214,252],"It":[103],"known":[105],"some":[107],"time":[108],"implies":[111,145],"\u03b1-strongly":[115],"compact":[116,152,171],"all":[118,154],"\u03b8":[121,123],"(where":[122],"least":[126],"cardinal":[127,138],"onto":[128],"which":[129],"\u03c9":[131],"cannot":[132,240],"be":[133,241],"mapped,":[134],"quite":[135],"large":[137],"under":[139,172],"AD),":[140],"R":[144],",":[149],"\u03b1-super":[151],"\u03b1":[155],"\u03b8.":[157],"A":[158],"key":[159],"open":[160],"question":[161],"had":[162],"been":[163],"whether":[164],"or":[165],"not":[166,234],"super":[170],"alone.":[174],"comments":[177],"on":[178,232],"method":[180,204,224,239],"in":[183,222],"several":[184],"different":[185],"ways.":[186],"\u00a72,":[188],"we":[189,217],"will":[190,218],"prove":[191],"compact,":[199],"then":[201],"generalize":[202],"to":[205,243],"show":[206,244],"3":[212],"-strongly":[213,251],"addition,":[216],"demonstrate":[219],"limitation":[221],"showing":[226],"possible":[229],"measures":[230],"obtained":[231],"normal,":[235],"extended":[242],"4":[250]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-07T06:01:17.266235","created_date":"2025-10-10T00:00:00"}