{"id":"https://openalex.org/W2031046912","doi":"https://doi.org/10.2307/2274277","title":"On the ultrafilters and ultrapowers of strong partition cardinals","display_name":"On the ultrafilters and ultrapowers of strong partition cardinals","publication_year":1984,"publication_date":"1984-12-01","ids":{"openalex":"https://openalex.org/W2031046912","doi":"https://doi.org/10.2307/2274277","mag":"2031046912"},"language":"en","primary_location":{"id":"doi:10.2307/2274277","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274277","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/A5054159138","display_name":"Jim Henle","orcid":null},"institutions":[{"id":"https://openalex.org/I202524275","display_name":"Smith College","ror":"https://ror.org/0497crr92","country_code":"US","type":"education","lineage":["https://openalex.org/I202524275"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"J.M. Henle","raw_affiliation_strings":["Smith College, Northampton, Massachusetts 01063","Smith College"],"affiliations":[{"raw_affiliation_string":"Smith College, Northampton, Massachusetts 01063","institution_ids":["https://openalex.org/I202524275"]},{"raw_affiliation_string":"Smith College","institution_ids":["https://openalex.org/I202524275"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034562840","display_name":"E. M. Kleinberg","orcid":null},"institutions":[{"id":"https://openalex.org/I63190737","display_name":"University at Buffalo, State University of New York","ror":"https://ror.org/01y64my43","country_code":"US","type":"education","lineage":["https://openalex.org/I63190737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"E.M. Kleinberg","raw_affiliation_strings":["State University of New York at Buffalo, Buffalo, New York 14214","State Univ. of New York at Buffalo"],"affiliations":[{"raw_affiliation_string":"State University of New York at Buffalo, Buffalo, New York 14214","institution_ids":["https://openalex.org/I63190737"]},{"raw_affiliation_string":"State Univ. of New York at Buffalo","institution_ids":["https://openalex.org/I63190737"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019019699","display_name":"Ronald Watro","orcid":null},"institutions":[{"id":"https://openalex.org/I7863295","display_name":"Villanova University","ror":"https://ror.org/02g7kd627","country_code":"US","type":"education","lineage":["https://openalex.org/I7863295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R.J. Watro","raw_affiliation_strings":["Villanova University, Villanova, Pennsylvania 19085","Villanova University"],"affiliations":[{"raw_affiliation_string":"Villanova University, Villanova, Pennsylvania 19085","institution_ids":["https://openalex.org/I7863295"]},{"raw_affiliation_string":"Villanova University","institution_ids":["https://openalex.org/I7863295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5054159138"],"corresponding_institution_ids":["https://openalex.org/I202524275"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1654629,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"49","issue":"4","first_page":"1268","last_page":"1272"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9977999925613403,"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":0.9977999925613403,"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":0.9814000129699707,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9690999984741211,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.8231106996536255},{"id":"https://openalex.org/keywords/ultrafilter","display_name":"Ultrafilter","score":0.8153877258300781},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.713091254234314},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6777635812759399},{"id":"https://openalex.org/keywords/uncountable-set","display_name":"Uncountable set","score":0.5622114539146423},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5307307839393616},{"id":"https://openalex.org/keywords/regular-cardinal","display_name":"Regular cardinal","score":0.47535985708236694},{"id":"https://openalex.org/keywords/order-type","display_name":"Order type","score":0.4324643015861511},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.423796147108078},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.2738707363605499},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.267591655254364},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.2105138599872589},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06430909037590027}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8231106996536255},{"id":"https://openalex.org/C87598191","wikidata":"https://www.wikidata.org/wiki/Q1571831","display_name":"Ultrafilter","level":2,"score":0.8153877258300781},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.713091254234314},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6777635812759399},{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.5622114539146423},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5307307839393616},{"id":"https://openalex.org/C89507440","wikidata":"https://www.wikidata.org/wiki/Q1193137","display_name":"Regular cardinal","level":2,"score":0.47535985708236694},{"id":"https://openalex.org/C138890893","wikidata":"https://www.wikidata.org/wiki/Q620006","display_name":"Order type","level":2,"score":0.4324643015861511},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.423796147108078},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.2738707363605499},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.267591655254364},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2105138599872589},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06430909037590027},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2274277","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274277","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/1183741704","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183741704","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":10,"referenced_works":["https://openalex.org/W8173881","https://openalex.org/W38810708","https://openalex.org/W129127956","https://openalex.org/W137575595","https://openalex.org/W572278001","https://openalex.org/W1990240363","https://openalex.org/W2035925255","https://openalex.org/W2769127010","https://openalex.org/W2918065189","https://openalex.org/W6609305928"],"related_works":["https://openalex.org/W2167408243","https://openalex.org/W1986962265","https://openalex.org/W4288278828","https://openalex.org/W4248353912","https://openalex.org/W2965212342","https://openalex.org/W1659717085","https://openalex.org/W2015103007","https://openalex.org/W4229892815","https://openalex.org/W4253415834","https://openalex.org/W2031046912"],"abstract_inverted_index":{"A":[0],"strong":[1,71,99,131,156,167,183],"partition":[2,13,72,100,132,157,168,184,251],"cardinal":[3,8,185],"is":[4,44,56,187,196,208,239],"an":[5,79],"uncountable":[6],"well-ordered":[7],"\u03ba":[9,16,18,21,24,29,186,195,204,219,228,230],"such":[10,42],"that":[11,88,104,181],"every":[12,191],"of":[14,23,36,41,49,70,84,92,111,194,224],"[":[15,227],"]":[17,229],"(the":[19],"size":[20,37],"subsets":[22],")":[25],"into":[26],"less":[27,233],"than":[28,234],"many":[30],"pieces":[31],"has":[32,121],"a":[33,89,182,209,241,249],"homogeneous":[34],"set":[35,61,126],"\u03ba.":[38],"The":[39,68,82,102],"existence":[40],"cardinals":[43,73,93,133,169],"inconsistent":[45],"with":[46,63,74,162],"the":[47,98,108,116,151,163,214,222,225,232],"axiom":[48,83],"choice,":[50],"and":[51,128,142,155,177],"our":[52],"work":[53],"concerning":[54,130,150],"them":[55],"carried":[57],"out":[58],"in":[59,107,137,172,189],"ZF":[60],"theory":[62,77],"just":[64],"dependent":[65],"choice":[66],"(DC).":[67],"consistency":[69],"this":[75,138],"weaker":[76],"remains":[78],"open":[80],"question.":[81],"determinacy":[85],"(AD)":[86],"implies":[87],"large":[90],"number":[91],"including":[94],"\u2135":[95],"1":[96],"have":[97],"property.":[101],"hypothesis":[103],"AD":[105,154],"holds":[106],"inner":[109],"model":[110],"constructible":[112],"sets":[113],"built":[114],"over":[115],"real":[117],"numbers":[118],"as":[119,170],"urelements":[120],"important":[122],"consequences":[123],"for":[124],"descriptive":[125],"theory,":[127],"results":[129,165],"are":[134],"often":[135],"applied":[136],"context.":[139],"Kechris":[140,143],"[4]":[141],"et":[144],"al.":[145],"[5]":[146],"contain":[147],"further":[148],"information":[149],"relationship":[152],"between":[153],"cardinals.":[158,256],"We":[159],"assume":[160],"familiarity":[161],"basic":[164],"on":[166,203,218,253],"developed":[171],"Kleinberg":[173],"[6],":[174],"[7],":[175],"[8]":[176],"Henle":[178],"[2].":[179],"Recall":[180],"measurable;":[188],"fact":[190],"stationary":[192],"subset":[193],"measure":[197,202],"one":[198],"under":[199,231],"some":[200],"normal":[201],".":[205],"If":[206],"\u03bc":[207,237],"countably":[210],"additive":[211],"ultrafilter":[212],"extending":[213],"closed":[215],"unbounded":[216],"filter":[217],",":[220],"then":[221],"length":[223],"ultrapower":[226],"almost":[235],"everywhere":[236],"ordering":[238],"again":[240],"measurable":[242,255],"cardinal.":[243],"In":[244],"\u00a71":[245],"below":[246],"we":[247],"establish":[248],"polarized":[250],"property":[252],"these":[254]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}