{"id":"https://openalex.org/W1979719505","doi":"https://doi.org/10.2307/2694968","title":"The canary tree revisited","display_name":"The canary tree revisited","publication_year":2001,"publication_date":"2001-12-01","ids":{"openalex":"https://openalex.org/W1979719505","doi":"https://doi.org/10.2307/2694968","mag":"1979719505"},"language":"en","primary_location":{"id":"doi:10.2307/2694968","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2694968","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/A5064743484","display_name":"Tapani Hyttinen","orcid":"https://orcid.org/0000-0002-5125-3839"},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]},{"id":"https://openalex.org/I2800229700","display_name":"Helsinki Institute of Physics","ror":"https://ror.org/01x2x1522","country_code":"FI","type":"facility","lineage":["https://openalex.org/I133731052","https://openalex.org/I2800229700","https://openalex.org/I63548447","https://openalex.org/I94722563","https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Tapani Hyttinen","raw_affiliation_strings":["Department of Mathematics, P.O. BOX 4, 00014 University of Helsinki, Finland, E-mail:","Department of Mathematics, P.O. BOX 4, 00014 University of Helsinki, Finland, E-mail: Tapani.Hyttinen@Helsinki.fi, E-mail: Mika.Rautila@Helsinki.fi"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, P.O. BOX 4, 00014 University of Helsinki, Finland, E-mail:","institution_ids":["https://openalex.org/I133731052","https://openalex.org/I2800229700"]},{"raw_affiliation_string":"Department of Mathematics, P.O. BOX 4, 00014 University of Helsinki, Finland, E-mail: Tapani.Hyttinen@Helsinki.fi, E-mail: Mika.Rautila@Helsinki.fi","institution_ids":["https://openalex.org/I133731052"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025061390","display_name":"Mika Rautila","orcid":null},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]},{"id":"https://openalex.org/I2800229700","display_name":"Helsinki Institute of Physics","ror":"https://ror.org/01x2x1522","country_code":"FI","type":"facility","lineage":["https://openalex.org/I133731052","https://openalex.org/I2800229700","https://openalex.org/I63548447","https://openalex.org/I94722563","https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Mika Rautila","raw_affiliation_strings":["Department of Mathematics, P.O. BOX 4, 00014 University of Helsinki, Finland, E-mail:","Department of Mathematics, P.O. BOX 4, 00014 University of Helsinki, Finland, E-mail: Tapani.Hyttinen@Helsinki.fi, E-mail: Mika.Rautila@Helsinki.fi"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, P.O. BOX 4, 00014 University of Helsinki, Finland, E-mail:","institution_ids":["https://openalex.org/I133731052","https://openalex.org/I2800229700"]},{"raw_affiliation_string":"Department of Mathematics, P.O. BOX 4, 00014 University of Helsinki, Finland, E-mail: Tapani.Hyttinen@Helsinki.fi, E-mail: Mika.Rautila@Helsinki.fi","institution_ids":["https://openalex.org/I133731052"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.11612532,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"66","issue":"4","first_page":"1677","last_page":"1694"},"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":0.9961000084877014,"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":0.9853000044822693,"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/uncountable-set","display_name":"Uncountable set","score":0.8420857787132263},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6795899868011475},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.6616159081459045},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3653346300125122},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.31671053171157837}],"concepts":[{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.8420857787132263},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6795899868011475},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.6616159081459045},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3653346300125122},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.31671053171157837},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2694968","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2694968","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/1183746618","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183746618","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":9,"referenced_works":["https://openalex.org/W34438034","https://openalex.org/W151695810","https://openalex.org/W1595388840","https://openalex.org/W1777877970","https://openalex.org/W1969238049","https://openalex.org/W2007936948","https://openalex.org/W2377287547","https://openalex.org/W4250879870","https://openalex.org/W6606203634"],"related_works":["https://openalex.org/W2080628627","https://openalex.org/W2960278316","https://openalex.org/W2171543968","https://openalex.org/W1978042415","https://openalex.org/W2345403094","https://openalex.org/W3086542228","https://openalex.org/W2017331178","https://openalex.org/W2183079734","https://openalex.org/W2088270774","https://openalex.org/W1999476205"],"abstract_inverted_index":{"Abstract.":[0],"We":[1,27],"generalize":[2],"the":[3,11,33],"result":[4],"of":[5,13,19],"Mekler":[6],"and":[7],"Shelah":[8],"[3]":[9],"that":[10],"existence":[12],"a":[14],"canary":[15],"tree":[16],"is":[17],"independent":[18],"ZFC":[20],"+":[21],"GCH":[22],"to":[23],"uncountable":[24],"regular":[25],"cardinals.":[26],"also":[28],"correct":[29],"an":[30],"error":[31],"from":[32],"original":[34],"proof.":[35]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
