{"id":"https://openalex.org/W2122314349","doi":"https://doi.org/10.2307/2272121","title":"On splitting stationary subsets of large cardinals","display_name":"On splitting stationary subsets of large cardinals","publication_year":1977,"publication_date":"1977-06-01","ids":{"openalex":"https://openalex.org/W2122314349","doi":"https://doi.org/10.2307/2272121","mag":"2122314349"},"language":"en","primary_location":{"id":"doi:10.2307/2272121","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2272121","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/A5001636447","display_name":"James E. Baumgartner","orcid":"https://orcid.org/0000-0002-9589-3504"},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"James E. Baumgartner","raw_affiliation_strings":["Dartmouth College, Hanover, New Hampshire 03755","Dartmouth College Hanover, New Hampshire 03755"],"affiliations":[{"raw_affiliation_string":"Dartmouth College, Hanover, New Hampshire 03755","institution_ids":["https://openalex.org/I107672454"]},{"raw_affiliation_string":"Dartmouth College Hanover, New Hampshire 03755","institution_ids":["https://openalex.org/I107672454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005176503","display_name":"Alan D. Taylor","orcid":"https://orcid.org/0000-0001-6866-0433"},"institutions":[{"id":"https://openalex.org/I177328695","display_name":"Union College","ror":"https://ror.org/058w5nk68","country_code":"US","type":"education","lineage":["https://openalex.org/I177328695"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alan D. Taylor","raw_affiliation_strings":["Union College, Schenectady, New York 12308"],"affiliations":[{"raw_affiliation_string":"Union College, Schenectady, New York 12308","institution_ids":["https://openalex.org/I177328695"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010825521","display_name":"Stanley Wagon","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":false,"raw_author_name":"Stanley Wagon","raw_affiliation_strings":["Smith College, Northampton, Massachusetts 01060"],"affiliations":[{"raw_affiliation_string":"Smith College, Northampton, Massachusetts 01060","institution_ids":["https://openalex.org/I202524275"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5001636447"],"corresponding_institution_ids":["https://openalex.org/I107672454"],"apc_list":null,"apc_paid":null,"fwci":2.6635,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.91807229,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"42","issue":"2","first_page":"203","last_page":"214"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9890999794006348,"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":0.9789999723434448,"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/uncountable-set","display_name":"Uncountable set","score":0.907706081867218},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7779922485351562},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.7298921942710876},{"id":"https://openalex.org/keywords/regular-cardinal","display_name":"Regular cardinal","score":0.6294212341308594},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5198822021484375},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.4496935307979584},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42328715324401855},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40543702244758606},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09293758869171143},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.0826992392539978},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.06453540921211243},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06070864200592041}],"concepts":[{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.907706081867218},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7779922485351562},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.7298921942710876},{"id":"https://openalex.org/C89507440","wikidata":"https://www.wikidata.org/wiki/Q1193137","display_name":"Regular cardinal","level":2,"score":0.6294212341308594},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5198822021484375},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.4496935307979584},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42328715324401855},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40543702244758606},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09293758869171143},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.0826992392539978},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.06453540921211243},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06070864200592041},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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:10.2307/2272121","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2272121","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/1183739946","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183739946","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W656854703","https://openalex.org/W1518517119","https://openalex.org/W1560317702","https://openalex.org/W1965874532","https://openalex.org/W2052196037","https://openalex.org/W2074199159","https://openalex.org/W2081896365","https://openalex.org/W2122092051","https://openalex.org/W4237640585","https://openalex.org/W4241720531","https://openalex.org/W4249167230","https://openalex.org/W6621949684","https://openalex.org/W6631167740"],"related_works":["https://openalex.org/W4289676933","https://openalex.org/W2950296149","https://openalex.org/W2885719937","https://openalex.org/W4297981628","https://openalex.org/W2952331208","https://openalex.org/W4298219619","https://openalex.org/W2097355897","https://openalex.org/W2167408243","https://openalex.org/W2567038806","https://openalex.org/W2557290701"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"\u03ba":[2,17,31,37,42,54,65,73,83,115,123,128,145,150,191,194],"denote":[3],"a":[4,68,144,157],"regular":[5],"uncountable":[6],"cardinal":[7,172,190],"and":[8,109],"NS":[9,27,52,89,120],"the":[10,22,99,111,184],"normal":[11,61,179],"ideal":[12,62,186],"of":[13,16,41,160],"nonstationary":[14],"subsets":[15,40],".":[18,173],"Our":[19,47],"results":[20],"concern":[21],"well-known":[23],"open":[24],"question":[25],"whether":[26],"fails":[28],"to":[29,94,104,177],"be":[30],"+":[32,38,55,124,195],"-saturated,":[33],"i.e.,":[34],"are":[35],"there":[36,66,155],"stationary":[39,69,158],"with":[43],"pairwise":[44],"intersections":[45],"nonstationary?":[46],"first":[48],"observation":[49],"is:":[50],"Theorem.":[51,113,126],"is":[53,67,116,121,129,151,156,192],"-":[56,134,146,170],"saturated":[57,147],"iff":[58],"for":[59],"every":[60],"J":[63,76],"on":[64,187],"set":[70,159],"A":[71,87],"\u2286":[72,82],"such":[74],"that":[75],"=":[77,79],"NS\u2223A":[78],"{":[80],"X":[81,85],":":[84],"\u2229":[86],"\u2208":[88],"}.":[90],"Turning":[91],"our":[92],"attention":[93],"large":[95],"cardinals,":[96],"we":[97],"extend":[98],"usual":[100],"(weak)":[101],"Mahlo":[102,118,162],"hierarchy":[103],"define":[105],"\u201cgreatly":[106],"Mahlo\u201d":[107],"cardinals":[108,163],"obtain":[110],"following:":[112],"If":[114,127],"greatly":[117,152,161],"then":[119,149],"not":[122,193],"-saturated.":[125,196],"ordinal":[130,166],"\u03a0":[131,167],"1":[132,133,168,169],"indescribable":[135,171],"(e.g.,":[136,140],"weakly":[137],"compact),":[138],"ethereal":[139],"subtle),":[141],"or":[142],"carries":[143],"ideal,":[148],"Mahlo.":[153],"Moreover,":[154],"below":[164],"any":[165],"These":[174],"methods":[175],"apply":[176],"other":[178],"ideals":[180],"as":[181],"well;":[182],"e.g.,":[183],"subtle":[185],"an":[188],"ineffable":[189]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}