{"id":"https://openalex.org/W2022950006","doi":"https://doi.org/10.2178/jsl/1190150050","title":"On essentially low, canonically well-generated Boolean algebras","display_name":"On essentially low, canonically well-generated Boolean algebras","publication_year":2002,"publication_date":"2002-03-01","ids":{"openalex":"https://openalex.org/W2022950006","doi":"https://doi.org/10.2178/jsl/1190150050","mag":"2022950006"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1190150050","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150050","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/A5050493936","display_name":"Robert Bonnet","orcid":null},"institutions":[{"id":"https://openalex.org/I70900168","display_name":"Universit\u00e9 Savoie Mont Blanc","ror":"https://ror.org/04gqg1a07","country_code":"FR","type":"education","lineage":["https://openalex.org/I70900168"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Robert Bonnet","raw_affiliation_strings":["Laboratoire De Math\u00e9matiques, Universit\u00e9 De Savoie, Le Bourget-Du-Lac, France, E-mail:","Laboratoire De Math\u00e9matiques, Universit\u00e9 De Savoie, Le Bourget-Du-Lac, France, E-mail: bonnet@in2p3.fr"],"affiliations":[{"raw_affiliation_string":"Laboratoire De Math\u00e9matiques, Universit\u00e9 De Savoie, Le Bourget-Du-Lac, France, E-mail:","institution_ids":["https://openalex.org/I70900168"]},{"raw_affiliation_string":"Laboratoire De Math\u00e9matiques, Universit\u00e9 De Savoie, Le Bourget-Du-Lac, France, E-mail: bonnet@in2p3.fr","institution_ids":["https://openalex.org/I70900168"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005194314","display_name":"Matatyahu Rubin","orcid":null},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Matatyahu Rubin","raw_affiliation_strings":["Department of Mathematics and CS, Ben Gurion University, Beer Sheva, Israel, E-mail:","Department of Mathematics and CS, Ben Gurion University, Beer Sheva, Israel, E-mail: matti@math.bgu.ac.il"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and CS, Ben Gurion University, Beer Sheva, Israel, E-mail:","institution_ids":["https://openalex.org/I124227911"]},{"raw_affiliation_string":"Department of Mathematics and CS, Ben Gurion University, Beer Sheva, Israel, E-mail: matti@math.bgu.ac.il","institution_ids":["https://openalex.org/I124227911"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050493936"],"corresponding_institution_ids":["https://openalex.org/I70900168"],"apc_list":null,"apc_paid":null,"fwci":0.9805,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.71529726,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"67","issue":"1","first_page":"369","last_page":"396"},"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9994999766349792,"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":0.9991000294685364,"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/stones-representation-theorem-for-boolean-algebras","display_name":"Stone's representation theorem for Boolean algebras","score":0.7076361775398254},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6978194713592529},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6114596724510193},{"id":"https://openalex.org/keywords/complete-boolean-algebra","display_name":"Complete Boolean algebra","score":0.6059702634811401},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.6017501354217529},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5886704921722412},{"id":"https://openalex.org/keywords/subalgebra","display_name":"Subalgebra","score":0.551287829875946},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.5308395624160767},{"id":"https://openalex.org/keywords/boolean-algebra","display_name":"Boolean algebra","score":0.48635584115982056},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48051366209983826},{"id":"https://openalex.org/keywords/boolean-algebras-canonically-defined","display_name":"Boolean algebras canonically defined","score":0.4382953643798828},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4310782253742218},{"id":"https://openalex.org/keywords/free-boolean-algebra","display_name":"Free Boolean algebra","score":0.4161882698535919},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.35598957538604736},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.2556355595588684},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1996811330318451},{"id":"https://openalex.org/keywords/filtered-algebra","display_name":"Filtered algebra","score":0.10112246870994568},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.05795937776565552}],"concepts":[{"id":"https://openalex.org/C10021369","wikidata":"https://www.wikidata.org/wiki/Q1166774","display_name":"Stone's representation theorem for Boolean algebras","level":5,"score":0.7076361775398254},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6978194713592529},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6114596724510193},{"id":"https://openalex.org/C81518389","wikidata":"https://www.wikidata.org/wiki/Q5156447","display_name":"Complete Boolean algebra","level":5,"score":0.6059702634811401},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.6017501354217529},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5886704921722412},{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.551287829875946},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.5308395624160767},{"id":"https://openalex.org/C39685927","wikidata":"https://www.wikidata.org/wiki/Q173183","display_name":"Boolean algebra","level":2,"score":0.48635584115982056},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48051366209983826},{"id":"https://openalex.org/C45503250","wikidata":"https://www.wikidata.org/wiki/Q4943350","display_name":"Boolean algebras canonically defined","level":5,"score":0.4382953643798828},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4310782253742218},{"id":"https://openalex.org/C188159880","wikidata":"https://www.wikidata.org/wiki/Q5499761","display_name":"Free Boolean algebra","level":5,"score":0.4161882698535919},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.35598957538604736},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2556355595588684},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1996811330318451},{"id":"https://openalex.org/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.10112246870994568},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.05795937776565552},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1190150050","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150050","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"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1190150050","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1190150050","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W795003239","https://openalex.org/W2038008480","https://openalex.org/W2044701145","https://openalex.org/W2914247088","https://openalex.org/W4255280388"],"related_works":["https://openalex.org/W2940617399","https://openalex.org/W2037090414","https://openalex.org/W2369221237","https://openalex.org/W4256012180","https://openalex.org/W2064028328","https://openalex.org/W2377493875","https://openalex.org/W2377302330","https://openalex.org/W2349635818","https://openalex.org/W176883546","https://openalex.org/W4243997191"],"abstract_inverted_index":{"Abstract":[0],"Let":[1,95,204],"B":[2,12,14,29,34,43,62,72,90,132,154,156,161,177,186,200,205,215,222,229,244,268,274,293,308,314],"be":[3,19,50,66,206],"a":[4,32,41,45,70,76,92,102,108,116,125,137,140,149,169,192,207,237,271,279,330],"superatomic":[5,226],"Boolean":[6,55,208,227,297,322],"algebra":[7,56,209,228,323],"(BA).":[8],"The":[9,58],"rank":[10,23,39,52,59],"of":[11,24,28,40,53,60,89,128,176,221,261,275,307],"(rk(":[13,44],")).":[15,46],"is":[16,47,63,75,93,124,139,162,181,187,216,223,230,257,294,309,315,324,333],"defined":[17,48,64],"to":[18,49,65,284],"the":[20,25,38,51,54,81,86,174,258,300],"Cantor":[21],"Bendixon":[22],"Stone":[26],"space":[27],".":[30,57,99,150,157,201,213],"If":[31,214,319],"\u2208":[33,71,98,143],"\u2212":[35,73],"{0},":[36],"then":[37,218,299,327],"in":[42,85],"0":[61],"\u22121.":[67],"An":[68],"element":[69],"{0}":[74],"generalized":[77],"atom":[78],",":[79,105,133],"if":[80,106,134,166,189,234,292],"last":[82],"nonzero":[83],"cardinal":[84,87,211],"sequence":[88,212],"\u21be":[91],"1.":[94,203,249],"a,":[96],"b":[97,104,112,118],"We":[100,158,183],"denote":[101],"\u02dc":[103],"rk(":[107,111,115,243],")":[109,113,247],"=":[110,114],"\u00b7":[117],").":[119],"A":[120,225],"subset":[121],"H":[122,144,171,180],"\u2286":[123],"complete":[126],"set":[127,272,283],"representatives":[129],"(CSR)":[130],"for":[131,135,153],"every":[136,219],"there":[138],"unique":[141],"h":[142,147],"such":[145,172,196,241],"that":[146,160,173,185,197,242,291],"~":[148],"Any":[151],"CSR":[152,170],"generates":[155,199],"say":[159,184],"canonically":[163],"well-generated":[164],"(CWG),":[165],"it":[167,190,235,328],"has":[168,191,236,329],"sublattice":[175,194],"generated":[178],"by":[179],"well-founded.":[182],"well-generated,":[188],"well-founded":[193],"L":[195,198],"Theorem":[202,250,254,288,317],"with":[210],"CWG,":[217,326],"subalgebra":[220,306,331],"CWG.":[224],"essentially":[231],"low":[232],"(ESL),":[233],"countable":[238],"ideal":[239],"I":[240,246],"/":[245],"\u2264":[248],"1":[251],"follows":[252],"from":[253,278],"2.9.":[255],"which":[256,332],"main":[259],"result":[260],"this":[262],"work.":[263],"For":[264],"an":[265,295,320],"ESL":[266,296,321],"BA":[267],"we":[269],"define":[270],"F":[273,313],"partial":[276],"functions":[277],"certain":[280],"countably":[281],"infinite":[282],"\u03c9":[285],"(Definition":[286],"2.8).":[287],"2.9":[289],"says":[290],"algebra,":[298],"following":[301],"are":[302],"equivalent.":[303],"(1)":[304],"Every":[305],"CWG:":[310],"and":[311],"(2)":[312],"bounded.":[316],"2.":[318],"not":[325,334],"well-generated.":[335]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
