{"id":"https://openalex.org/W2065096910","doi":"https://doi.org/10.1002/malq.201010014","title":"Superatomic Boolean algebras constructed from strongly unbounded functions","display_name":"Superatomic Boolean algebras constructed from strongly unbounded functions","publication_year":2011,"publication_date":"2011-07-25","ids":{"openalex":"https://openalex.org/W2065096910","doi":"https://doi.org/10.1002/malq.201010014","mag":"2065096910"},"language":"en","primary_location":{"id":"doi:10.1002/malq.201010014","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201010014","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":true,"oa_status":"green","oa_url":"https://ddd.uab.cat/record/70561","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100716534","display_name":"Juan Carlos Mart\u00ednez","orcid":"https://orcid.org/0000-0002-9304-9959"},"institutions":[{"id":"https://openalex.org/I71999127","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57","country_code":"ES","type":"education","lineage":["https://openalex.org/I71999127"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Juan Carlos Mart\u00ednez","raw_affiliation_strings":["Facultat de Matema\u0300tiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain","Facultat de Matem\u00e0tiques, Universitat de Barcelona, Gran Via, 585, 08007-Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Facultat de Matema\u0300tiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain","institution_ids":["https://openalex.org/I71999127"]},{"raw_affiliation_string":"Facultat de Matem\u00e0tiques, Universitat de Barcelona, Gran Via, 585, 08007-Barcelona, Spain","institution_ids":["https://openalex.org/I71999127"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060501499","display_name":"Lajos Soukup","orcid":"https://orcid.org/0000-0002-3975-0293"},"institutions":[{"id":"https://openalex.org/I71999127","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57","country_code":"ES","type":"education","lineage":["https://openalex.org/I71999127"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Lajos Soukup","raw_affiliation_strings":["Facultat de Matema\u0300tiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain","Facultat de Matem\u00e0tiques, Universitat de Barcelona, Gran Via, 585, 08007-Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Facultat de Matema\u0300tiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain","institution_ids":["https://openalex.org/I71999127"]},{"raw_affiliation_string":"Facultat de Matem\u00e0tiques, Universitat de Barcelona, Gran Via, 585, 08007-Barcelona, Spain","institution_ids":["https://openalex.org/I71999127"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5060501499","https://openalex.org/A5100716534"],"corresponding_institution_ids":["https://openalex.org/I71999127"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.3773,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.59054065,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"57","issue":"5","first_page":"456","last_page":"469"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9969000220298767,"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":0.9969000220298767,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.996399998664856,"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"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.993399977684021,"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/omega","display_name":"Omega","score":0.759372889995575},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.597321629524231},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5756196975708008},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.4232070744037628},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.40452951192855835},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32018494606018066},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.23111289739608765},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17182019352912903},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11085876822471619}],"concepts":[{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.759372889995575},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.597321629524231},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5756196975708008},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.4232070744037628},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.40452951192855835},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32018494606018066},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.23111289739608765},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17182019352912903},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11085876822471619}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1002/malq.201010014","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201010014","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"},{"id":"pmh:oai:ddd.uab.cat:70561","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/70561","pdf_url":"https://ddd.uab.cat/record/70561","source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:dnet:uabarcelona_::9adffe48d4f310a5a11f33157512c417","is_oa":true,"landing_page_url":"http://ddd.uab.cat/record/70561","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:recercat.cat:2072/150324","is_oa":true,"landing_page_url":"http://hdl.handle.net/2072/150324","pdf_url":null,"source":{"id":"https://openalex.org/S4306402147","display_name":"RECERCAT (Consorci de Serveis Universitaris de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210090028","host_organization_name":"Consorci de Serveis Universitaris de Catalunya","host_organization_lineage":["https://openalex.org/I4210090028"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/preprint"}],"best_oa_location":{"id":"pmh:oai:ddd.uab.cat:70561","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/70561","pdf_url":"https://ddd.uab.cat/record/70561","source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320335162","display_name":"Departament d'Universitats, Recerca i Societat de la Informaci\u00f3","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2065096910.pdf"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1493437558","https://openalex.org/W1496446432","https://openalex.org/W1969856046","https://openalex.org/W1998841441","https://openalex.org/W2000762087","https://openalex.org/W2011407188","https://openalex.org/W2061800462","https://openalex.org/W2595275026","https://openalex.org/W2914247088"],"related_works":["https://openalex.org/W238609530","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2734192830","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W3016395638"],"abstract_inverted_index":{"Using":[0],"Koszmider's":[1],"strongly":[2],"unbounded":[3],"functions,":[4],"we":[5],"show":[6],"the":[7],"following":[8],"consistency":[9],"result:":[10],"Suppose":[11],"that":[12,19,61],"\u03ba,":[13],"\u03bb":[14],"are":[15],"infinite":[16],"cardinals":[17],"such":[18,60],"\u03ba++":[20,41],"+":[21,66],"\u2264":[22,38],"\u03bb,":[23],"\u03ba<\u03ba":[24],"=":[25,29,44,64,71,82],"\u03ba":[26],"and":[27,31,42,78,105],"2\u03ba":[28],"\u03ba+,":[30],"\u03b7":[32,39,77],"is":[33,53,85],"an":[34],"ordinal":[35],"with":[36,91],"\u03ba+":[37],"<":[40,76],"cf(\u03b7)":[43],"\u03ba+.":[45],"Then,":[46],"in":[47],"some":[48],"cardinal-preserving":[49],"generic":[50],"extension":[51],"there":[52,84],"a":[54,86],"superatomic":[55,120],"Boolean":[56,121],"algebra":[57],"\\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathcal":[58],"B$\\end{document}":[59],"\\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathrm{ht}(\\mathcal":[62],"B)":[63,70,81],"\\eta":[65],"1$\\end{document},":[67],"\\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathrm{wd}_{\\alpha":[68],"}(\\mathcal":[69,80],"\\kappa$\\end{document}":[72],"for":[73],"every":[74],"\u03b1":[75],"\\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathrm{wd}_{\\eta":[79],"\\lambda$\\end{document}(i.e.,":[83],"locally":[87],"compact":[88],"scattered":[89],"space":[90],"cardinal":[92,117],"sequence":[93],"\u3008\u03ba\u3009\u03b7\u2322\ufe01\u3008\u03bb\u3009).":[94],"Especially,":[95],"\\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\langle":[96,106],"{\\omega":[97,103,107,113],"}\\rangle":[98],"_{{\\omega":[99,109],"}_1}{}^{\\smallfrown":[100],"}":[101,111],"\\langle":[102,112],"}_3\\rangle$\\end{document}":[104],"}_1\\rangle":[108],"}_2}{}^{\\smallfrown":[110],"}_4\\rangle$\\end{document}":[114],"can":[115],"be":[116],"sequences":[118],"of":[119],"algebras.":[122]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}