{"id":"https://openalex.org/W2000390507","doi":"https://doi.org/10.2307/2273824","title":"Partition properties of <b>M</b>-ultrafilters and ideals","display_name":"Partition properties of <b>M</b>-ultrafilters and ideals","publication_year":1987,"publication_date":"1987-12-01","ids":{"openalex":"https://openalex.org/W2000390507","doi":"https://doi.org/10.2307/2273824","mag":"2000390507"},"language":"en","primary_location":{"id":"doi:10.2307/2273824","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273824","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/A5111402915","display_name":"Joji Takahashi","orcid":null},"institutions":[{"id":"https://openalex.org/I164061489","display_name":"University of Papua New Guinea","ror":"https://ror.org/05jxf0p38","country_code":"PG","type":"education","lineage":["https://openalex.org/I164061489"]}],"countries":["PG"],"is_corresponding":true,"raw_author_name":"Joji Takahashi","raw_affiliation_strings":["Department of Mathematics, University of Papua New Guinea, Port Moresby, Papua New Guinea","University of Papua New Guinea ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Papua New Guinea, Port Moresby, Papua New Guinea","institution_ids":["https://openalex.org/I164061489"]},{"raw_affiliation_string":"University of Papua New Guinea ,","institution_ids":["https://openalex.org/I164061489"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111402915"],"corresponding_institution_ids":["https://openalex.org/I164061489"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13344739,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"52","issue":"4","first_page":"897","last_page":"907"},"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9933000206947327,"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":0.9886999726295471,"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/ultrafilter","display_name":"Ultrafilter","score":0.9244953989982605},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8342699408531189},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.6925505995750427},{"id":"https://openalex.org/keywords/uncountable-set","display_name":"Uncountable set","score":0.6518434882164001},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.6031936407089233},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.567436933517456},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5196400880813599},{"id":"https://openalex.org/keywords/regular-cardinal","display_name":"Regular cardinal","score":0.48937052488327026},{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.42308205366134644},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4082947373390198},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.29021531343460083},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.28537505865097046},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.2554352879524231},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08359724283218384}],"concepts":[{"id":"https://openalex.org/C87598191","wikidata":"https://www.wikidata.org/wiki/Q1571831","display_name":"Ultrafilter","level":2,"score":0.9244953989982605},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8342699408531189},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.6925505995750427},{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.6518434882164001},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.6031936407089233},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.567436933517456},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5196400880813599},{"id":"https://openalex.org/C89507440","wikidata":"https://www.wikidata.org/wiki/Q1193137","display_name":"Regular cardinal","level":2,"score":0.48937052488327026},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.42308205366134644},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4082947373390198},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.29021531343460083},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.28537505865097046},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.2554352879524231},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08359724283218384},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2273824","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273824","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W612096478","https://openalex.org/W1484181842","https://openalex.org/W1498144540","https://openalex.org/W1965874532","https://openalex.org/W2009308509","https://openalex.org/W2042583800","https://openalex.org/W2083782312","https://openalex.org/W2153689630","https://openalex.org/W2218778419","https://openalex.org/W2297908936","https://openalex.org/W6628798026"],"related_works":["https://openalex.org/W4289676933","https://openalex.org/W2950296149","https://openalex.org/W4301309805","https://openalex.org/W2167408243","https://openalex.org/W1986962265","https://openalex.org/W4288278828","https://openalex.org/W4248353912","https://openalex.org/W2965212342","https://openalex.org/W2015103007","https://openalex.org/W4229892815"],"abstract_inverted_index":{"As":[0],"is":[1,19,47,91,99,149,153,190,238],"well":[2],"known,":[3],"the":[4,57,63,85,89,94,102,111,166,194,200,204,209,212],"following":[5],"are":[6,142,221],"equivalent":[7],"for":[8,67],"any":[9],"uniform":[10,179],"ultrafilter":[11],"U":[12,18,22,26],"on":[13,182],"an":[14,183],"uncountable":[15],"cardinal:":[16],"(i)":[17],"selective;":[20],"(ii)":[21],"\u2192":[23,27,171,175],";":[24],"(iii)":[25],".":[28,219],"In":[29,160,240],"\u00a71":[30,198],"of":[31,40,51,59,104,147,165,178,197,211,227,231,266],"this":[32,36],"paper,":[33],"we":[34,123,162],"consider":[35],"result":[37,86],"in":[38,203],"terms":[39],"M":[41,46,68,75,98,137,253,260],"-ultrafilters":[42,69,76],"(Definition":[43,70,129,176],"1.1),":[44],"where":[45],"a":[48,248,263],"transitive":[49,264],"model":[50,206,265],"ZFC":[52],"(Zermelo-Fraenkel":[53],"set":[54,236],"theory":[55,237],"with":[56],"axiom":[58],"choice).":[60],"We":[61],"define":[62],"partition":[64,167],"properties":[65,80,113,168],"and":[66,72,119,172,230,254],"1.3),":[71],"characterize":[73],"those":[74],"that":[77,84,97,110,258],"possess":[78],"these":[79],"(Theorem":[81,187],"1.5)":[82],"so":[83],"mentioned":[87],"at":[88],"beginning":[90],"subsumed":[92],"as":[93],"special":[95],"case":[96],"V":[100,139],",":[101],"universe":[103],"all":[105],"sets.":[106],"It":[107],"turns":[108],"out":[109],"two":[112],"have":[114],"to":[115,125,199,223,244],"be":[116,245],"handled":[117],"separately,":[118],"that,":[120],"besides":[121],"selectivity,":[122],"need":[124],"formulate":[126],"additional":[127],"conditions":[128,133],"1.4).":[130],"The":[131],"extra":[132],"become":[134],"superfluous":[135],"when":[136],"=":[138],"because":[140],"they":[141],"then":[143],"trivially":[144],"satisfied.":[145],"One":[146],"them":[148],"nothing":[150],"new;":[151],"it":[152,242],"none":[154],"other":[155],"than":[156],"Kunen's":[157],"iterability-of-ultrapowers":[158],"condition.":[159],"\u00a72,":[161],"obtain":[163],"characterizations":[164,226],"I":[169,173,181,218],"+":[170,174],"2.3)":[177],"ideals":[180],"infinite":[184],"cardinal":[185],"\u03ba":[186,216],"2.6).":[188],"This":[189],"done":[191],"by":[192,247],"applying":[193],"main":[195],"results":[196],"canonical":[201],"-ultrafilter":[202],"Boolean-valued":[205],"constructed":[207],"from":[208],"completion":[210],"quotient":[213],"algebra":[214],"P(":[215],")/":[217],"They":[220],"related":[222],"certain":[224],"known":[225],"weakly":[228],"compact":[229],"Ramsey":[232],"cardinals.":[233],"Our":[234],"basic":[235],"ZFC.":[239,267],"\u00a71,":[241],"has":[243],"supplemented":[246],"new":[249,255],"unary":[250],"predicate":[251],"symbol":[252],"nonlogical":[256],"axioms":[257],"make":[259],"look":[261],"like":[262]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
