{"id":"https://openalex.org/W1968238504","doi":"https://doi.org/10.1002/malq.19990450208","title":"Partition Complete Boolean Algebras and Almost Compact Cardinals","display_name":"Partition Complete Boolean Algebras and Almost Compact Cardinals","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W1968238504","doi":"https://doi.org/10.1002/malq.19990450208","mag":"1968238504"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19990450208","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19990450208","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/A5004708077","display_name":"Peter Jipsen","orcid":"https://orcid.org/0000-0001-8608-808X"},"institutions":[{"id":"https://openalex.org/I157614274","display_name":"University of Cape Town","ror":"https://ror.org/03p74gp79","country_code":"ZA","type":"education","lineage":["https://openalex.org/I157614274"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Peter Jipsen","raw_affiliation_strings":["Department of Mathematics and Applied Mathematics, University of Cape Town Rondebosch 7701, South Africa","Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7701 (South Africa)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, University of Cape Town Rondebosch 7701, South Africa","institution_ids":["https://openalex.org/I157614274"]},{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7701 (South Africa)","institution_ids":["https://openalex.org/I157614274"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080633784","display_name":"H E Rose","orcid":null},"institutions":[{"id":"https://openalex.org/I157614274","display_name":"University of Cape Town","ror":"https://ror.org/03p74gp79","country_code":"ZA","type":"education","lineage":["https://openalex.org/I157614274"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Henry Rose","raw_affiliation_strings":["Department of Mathematics and Applied Mathematics, University of Cape Town Rondebosch 7701, South Africa","Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7701 (South Africa)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, University of Cape Town Rondebosch 7701, South Africa","institution_ids":["https://openalex.org/I157614274"]},{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7701 (South Africa)","institution_ids":["https://openalex.org/I157614274"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I157614274"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.4806,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.55407029,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"45","issue":"2","first_page":"241","last_page":"255"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9842000007629395,"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":0.8812075257301331},{"id":"https://openalex.org/keywords/complete-boolean-algebra","display_name":"Complete Boolean algebra","score":0.7378619313240051},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.7243922352790833},{"id":"https://openalex.org/keywords/free-boolean-algebra","display_name":"Free Boolean algebra","score":0.7214134931564331},{"id":"https://openalex.org/keywords/boolean-algebras-canonically-defined","display_name":"Boolean algebras canonically defined","score":0.7211853265762329},{"id":"https://openalex.org/keywords/distributivity","display_name":"Distributivity","score":0.7209917306900024},{"id":"https://openalex.org/keywords/stones-representation-theorem-for-boolean-algebras","display_name":"Stone's representation theorem for Boolean algebras","score":0.7034957408905029},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.5900877714157104},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.5407329797744751},{"id":"https://openalex.org/keywords/boolean-algebra","display_name":"Boolean algebra","score":0.5212967395782471},{"id":"https://openalex.org/keywords/ultrafilter","display_name":"Ultrafilter","score":0.4958833158016205},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.47112083435058594},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4691670536994934},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44996756315231323},{"id":"https://openalex.org/keywords/interior-algebra","display_name":"Interior algebra","score":0.4171534478664398},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32349613308906555},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.24953815340995789},{"id":"https://openalex.org/keywords/division-algebra","display_name":"Division algebra","score":0.1937422752380371},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.11799120903015137},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.09279677271842957}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8812075257301331},{"id":"https://openalex.org/C81518389","wikidata":"https://www.wikidata.org/wiki/Q5156447","display_name":"Complete Boolean algebra","level":5,"score":0.7378619313240051},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.7243922352790833},{"id":"https://openalex.org/C188159880","wikidata":"https://www.wikidata.org/wiki/Q5499761","display_name":"Free Boolean algebra","level":5,"score":0.7214134931564331},{"id":"https://openalex.org/C45503250","wikidata":"https://www.wikidata.org/wiki/Q4943350","display_name":"Boolean algebras canonically defined","level":5,"score":0.7211853265762329},{"id":"https://openalex.org/C138390121","wikidata":"https://www.wikidata.org/wiki/Q5283219","display_name":"Distributivity","level":3,"score":0.7209917306900024},{"id":"https://openalex.org/C10021369","wikidata":"https://www.wikidata.org/wiki/Q1166774","display_name":"Stone's representation theorem for Boolean algebras","level":5,"score":0.7034957408905029},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.5900877714157104},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.5407329797744751},{"id":"https://openalex.org/C39685927","wikidata":"https://www.wikidata.org/wiki/Q173183","display_name":"Boolean algebra","level":2,"score":0.5212967395782471},{"id":"https://openalex.org/C87598191","wikidata":"https://www.wikidata.org/wiki/Q1571831","display_name":"Ultrafilter","level":2,"score":0.4958833158016205},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.47112083435058594},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4691670536994934},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44996756315231323},{"id":"https://openalex.org/C203254541","wikidata":"https://www.wikidata.org/wiki/Q10894825","display_name":"Interior algebra","level":5,"score":0.4171534478664398},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32349613308906555},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.24953815340995789},{"id":"https://openalex.org/C138354692","wikidata":"https://www.wikidata.org/wiki/Q1231309","display_name":"Division algebra","level":4,"score":0.1937422752380371},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.11799120903015137},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.09279677271842957},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.19990450208","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19990450208","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1498144540","https://openalex.org/W1756106495","https://openalex.org/W2914247088","https://openalex.org/W4231952429"],"related_works":["https://openalex.org/W2064128553","https://openalex.org/W11504065","https://openalex.org/W2951697398","https://openalex.org/W2785885914","https://openalex.org/W4300190062","https://openalex.org/W2030362615","https://openalex.org/W1496446432","https://openalex.org/W2123065381","https://openalex.org/W1147302066","https://openalex.org/W1590716824"],"abstract_inverted_index":{"Abstract":[0],"For":[1,57,98],"an":[2,67,75],"infinite":[3],"cardinal":[4],"K":[5,10,25,30,46,53,59,69,80,96,101,105,110,116,119,123,127],"a":[6,29],"stronger":[7],"version":[8],"of":[9,78,88],"\u2010distributivity":[11],"for":[12,50,93,136],"Boolean":[13,33,43,72],"algebras,":[14],"called":[15],"k\u2010partition":[16],"completeness,":[17,85],"is":[18,28,36,45,64,74,91,106,111,117,124,128,133],"defined":[19],"and":[20,49,114],"investigated":[21],"(e.":[22],"g.":[23],"every":[24,39],"\u2010Suslin":[26],"algebra":[27,44,73],"\u2010partition":[31,41,70],"complete":[32,42,71],"algebra).":[34],"It":[35],"shown":[37],"that":[38,66,104],"k":[40],"\u2010weakly":[47],"representable,":[48],"strongly":[51,99,129],"inaccessible":[52,100],"these":[54],"concepts":[55],"coincide.":[56],"regular":[58],"\u2265":[60,95,139],"u":[61],",":[62],"it":[63,132],"proved":[65],"atomless":[68],"updirected":[76],"union":[77],"basic":[79],"\u2010tree":[81],"algebras.":[82],"Using":[83],"K\u2010partition":[84],"the":[86],"concept":[87],"\u03b3\u2010almost":[89,134],"compactness":[90],"introduced":[92],"\u03b3":[94,138],".":[97],"we":[102],"show":[103],"K\u2010almost":[107],"compact":[108,130,135],"iff":[109,131],"weakly":[112],"compact,":[113,121],"if":[115],"2":[118],"\u2010almost":[120],"then":[122],"measurable.":[125],"Further":[126],"all":[137],"K.":[140]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
