{"id":"https://openalex.org/W2061709388","doi":"https://doi.org/10.2307/2275613","title":"Possible PCF algebras","display_name":"Possible PCF algebras","publication_year":1996,"publication_date":"1996-03-01","ids":{"openalex":"https://openalex.org/W2061709388","doi":"https://doi.org/10.2307/2275613","mag":"2061709388"},"language":"en","primary_location":{"id":"doi:10.2307/2275613","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275613","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/A5079801056","display_name":"Thomas Jech","orcid":null},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thomas Jech","raw_affiliation_strings":["Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA, E-mail:","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024923217","display_name":"Saharon Shelah","orcid":"https://orcid.org/0000-0003-0462-3152"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]},{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL","US"],"is_corresponding":false,"raw_author_name":"Saharon Shelah","raw_affiliation_strings":["Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA, E-mail:","School of Mathematics, The Hebrew University, Jerusalem, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA, E-mail:","institution_ids":["https://openalex.org/I102322142"]},{"raw_affiliation_string":"School of Mathematics, The Hebrew University, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":1.475,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.82910507,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"61","issue":"1","first_page":"313","last_page":"317"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9977999925613403,"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"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9977999925613403,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9922999739646912,"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":0.9879999756813049,"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/mathematics","display_name":"Mathematics","score":0.7707215547561646},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.7335221171379089},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6426920294761658},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6065571904182434},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5468074083328247},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5106235146522522},{"id":"https://openalex.org/keywords/existential-quantification","display_name":"Existential quantification","score":0.4721660315990448},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.466980904340744},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.4622392952442169},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.048474401235580444}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7707215547561646},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.7335221171379089},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6426920294761658},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6065571904182434},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5468074083328247},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5106235146522522},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.4721660315990448},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.466980904340744},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.4622392952442169},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.048474401235580444},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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":1,"locations":[{"id":"doi:10.2307/2275613","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275613","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":7,"referenced_works":["https://openalex.org/W2025890236","https://openalex.org/W2037540270","https://openalex.org/W2046051057","https://openalex.org/W2314333333","https://openalex.org/W2592587535","https://openalex.org/W4248490242","https://openalex.org/W4388284830"],"related_works":["https://openalex.org/W2950866767","https://openalex.org/W4299610791","https://openalex.org/W1631776469","https://openalex.org/W3106300234","https://openalex.org/W3019662020","https://openalex.org/W4281680667","https://openalex.org/W2890272564","https://openalex.org/W2168495785","https://openalex.org/W2788924535","https://openalex.org/W1977905610"],"abstract_inverted_index":{"Abstract":[0],"There":[1],"exists":[2],"a":[3,18,38],"family":[4],"of":[5,7],"sets":[6],"countable":[8],"ordinals":[9],"such":[10],"that:":[11],"(1)":[12],"maxB\u03b1=\u03b1,":[13],"(2)":[14],"if\u03b1\u2208B\u03b2thenB\u03b1\u2286B\u03b2,":[15],"(3)":[16],"if\u03bb\u2264\u03b1and\u03bbis":[17],"limit":[19],"ordinal":[20],"thenB\u03b1\u2229\u03bbis":[21],"not":[22],"in":[23],"the":[24,31],"ideal":[25],"generated":[26],"by":[27,30],"theB\u03b2,\u03b2<\u03b1,":[28],"and":[29],"bounded":[32],"subsets":[33],"of\u03bb,":[34],"(4)":[35],"there":[36],"is":[37],"partition":[39],"of\u03c91such":[40],"that":[41],"for":[42],"every\u03b1and":[43],"everyn,B\u03b1\u2229Anis":[44],"finite.":[45]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
