{"id":"https://openalex.org/W4253438498","doi":"https://doi.org/10.2307/2271949","title":"Saturated ideals","display_name":"Saturated ideals","publication_year":1978,"publication_date":"1978-03-01","ids":{"openalex":"https://openalex.org/W4253438498","doi":"https://doi.org/10.2307/2271949"},"language":"en","primary_location":{"id":"doi:10.2307/2271949","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271949","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/A5022605683","display_name":"Kenneth Kunen","orcid":null},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Kenneth Kunen","raw_affiliation_strings":["University of Wisconsin-Madison, Madison, Wisconsin 53706"],"affiliations":[{"raw_affiliation_string":"University of Wisconsin-Madison, Madison, Wisconsin 53706","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022605683"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":6.7127,"has_fulltext":false,"cited_by_count":117,"citation_normalized_percentile":{"value":0.97782178,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"43","issue":"1","first_page":"65","last_page":"76"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9986000061035156,"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":0.9986000061035156,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9922000169754028,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9905999898910522,"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/cardinality","display_name":"Cardinality (data modeling)","score":0.7582353353500366},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7167803645133972},{"id":"https://openalex.org/keywords/complete-boolean-algebra","display_name":"Complete Boolean algebra","score":0.6761723160743713},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.6717299222946167},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.623152494430542},{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.615780770778656},{"id":"https://openalex.org/keywords/stones-representation-theorem-for-boolean-algebras","display_name":"Stone's representation theorem for Boolean algebras","score":0.5657758116722107},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5619124174118042},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5260491371154785},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.5196691751480103},{"id":"https://openalex.org/keywords/boolean-algebra","display_name":"Boolean algebra","score":0.49365052580833435},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.49221912026405334},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4625844657421112},{"id":"https://openalex.org/keywords/free-boolean-algebra","display_name":"Free Boolean algebra","score":0.421896755695343},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37327927350997925},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32133084535598755},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28852683305740356},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.156032532453537},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14377665519714355},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.0835832953453064},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.0823897123336792}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.7582353353500366},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7167803645133972},{"id":"https://openalex.org/C81518389","wikidata":"https://www.wikidata.org/wiki/Q5156447","display_name":"Complete Boolean algebra","level":5,"score":0.6761723160743713},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.6717299222946167},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.623152494430542},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.615780770778656},{"id":"https://openalex.org/C10021369","wikidata":"https://www.wikidata.org/wiki/Q1166774","display_name":"Stone's representation theorem for Boolean algebras","level":5,"score":0.5657758116722107},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5619124174118042},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5260491371154785},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.5196691751480103},{"id":"https://openalex.org/C39685927","wikidata":"https://www.wikidata.org/wiki/Q173183","display_name":"Boolean algebra","level":2,"score":0.49365052580833435},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.49221912026405334},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4625844657421112},{"id":"https://openalex.org/C188159880","wikidata":"https://www.wikidata.org/wiki/Q5499761","display_name":"Free Boolean algebra","level":5,"score":0.421896755695343},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37327927350997925},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32133084535598755},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28852683305740356},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.156032532453537},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14377665519714355},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.0835832953453064},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0823897123336792},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2271949","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271949","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W656854703","https://openalex.org/W1613162937","https://openalex.org/W1965874532","https://openalex.org/W1975695422","https://openalex.org/W2030061379","https://openalex.org/W2084019437","https://openalex.org/W2110407978","https://openalex.org/W2122092051","https://openalex.org/W3151639028","https://openalex.org/W4249167230","https://openalex.org/W4291439952","https://openalex.org/W4298308357","https://openalex.org/W6621949684"],"related_works":["https://openalex.org/W2940617399","https://openalex.org/W2037090414","https://openalex.org/W2369221237","https://openalex.org/W2377493875","https://openalex.org/W2349635818","https://openalex.org/W4243997191","https://openalex.org/W2064028328","https://openalex.org/W2377302330","https://openalex.org/W4256012180","https://openalex.org/W2740171735"],"abstract_inverted_index":{"In":[0,167],"this":[1],"paper,":[2],"we":[3,71],"give":[4],"consistency":[5],"proofs":[6],"for":[7,19,107],"the":[8,20,51,56,78,100,159,173,179],"existence":[9,21],"of":[10,22,77,97,126,143,145,146],"a":[11,95,132,136,155],"\u03ba-saturated":[12],"ideal":[13,27],"on":[14,28,42],"an":[15,23,35],"inaccessible":[16],"\u03ba,":[17],"and":[18,61,135],"\u03c9":[24,29],"2":[25],"-saturated":[26],"1":[30],".":[31,47,108,166],"We":[32,48,103],"also":[33],"include":[34],"historical":[36],"survey":[37],"outlining":[38],"other":[39],"known":[40],"results":[41],"saturated":[43],"ideals.":[44],"\u00a71.":[45],"Forcing":[46],"assume":[49],"that":[50],"reader":[52],"is":[53,94,99,120,139,154,158,175,178],"familiar":[54],"with":[55,171],"usual":[57],"techniques":[58],"in":[59,161,164],"forcing":[60],"Boolean-valued":[62,180],"models":[63],"(see":[64],"Jech":[65],"[3]":[66],"or":[67],"Rosser":[68],"[11]),":[69],"so":[70],"shall":[72],"just":[73],"specify":[74],"here":[75],"some":[76],"less":[79,128,148],"standard":[80],"notation.":[81],"\u201ccBa\u201d":[82],"abbreviates":[83],"\u201ccomplete":[84],"Boolean":[85,137],"algebra\u201d.":[86],"If":[87,153],"P":[88,91,106,119],"(=":[89],"\u2039":[90],",":[92],"&lt;\u203a)":[93],"notion":[96],"forcing,":[98],"associated":[101],"cBa.":[102],"write":[104],"V":[105,165,183],"Notions":[109],"like":[110],"\u03ba-closed,":[111],"\u03ba-complete,":[112],"etc.":[113],"always":[114,151],"mean":[115],"&lt;":[116],"\u03ba.":[117],"Thus,":[118],"\u03ba-closed":[121],"iff":[122,141],"every":[123],"decreasing":[124],"chain":[125],"length":[127],"than":[129,149],"\u03ba":[130,150],"has":[131],"lower":[133],"bound,":[134],"algebra":[138],"\u03ba-complete":[140],"sups":[142],"subsets":[144],"cardinality":[147],"exist.":[152],"cBa,":[156],"x\u030c":[157],"object":[160],"representing":[162,182],"x":[163],"many":[168],"cases,":[169],"especially":[170],"ordinals,":[172],"\u030c":[174],"dropped.":[176],"V\u030c":[177],"class":[181],"\u2014":[184],"i.e.,":[185]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":19},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-03-11T06:11:40.159057","created_date":"2022-05-12T00:00:00"}
