{"id":"https://openalex.org/W2065342370","doi":"https://doi.org/10.2178/bsl/1294186662","title":"Combinatorial Dichotomies in Set Theory","display_name":"Combinatorial Dichotomies in Set Theory","publication_year":2011,"publication_date":"2011-01-05","ids":{"openalex":"https://openalex.org/W2065342370","doi":"https://doi.org/10.2178/bsl/1294186662","mag":"2065342370"},"language":"en","primary_location":{"id":"doi:10.2178/bsl/1294186662","is_oa":true,"landing_page_url":"https://doi.org/10.2178/bsl/1294186662","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D1E79287F8D3E93B43955455930B4A7C/S1079898600000627a.pdf/div-class-title-combinatorial-dichotomies-in-set-theory-div.pdf","source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"The Bulletin of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D1E79287F8D3E93B43955455930B4A7C/S1079898600000627a.pdf/div-class-title-combinatorial-dichotomies-in-set-theory-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018265011","display_name":"Stevo Todor\u010devi\u0107","orcid":"https://orcid.org/0000-0003-4543-7962"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]}],"countries":["CA","FR"],"is_corresponding":true,"raw_author_name":"Stevo Todorcevic","raw_affiliation_strings":["Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada, and Universit\u00e9 Paris 7, CNRS \u2013 FRE 3233, 75251 Paris, France, E-mail:","Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada, and Universit\u00e9 Paris 7, CNRS \u2013 FRE 3233, 75251 Paris, France, E-mail/i: stevo@math.utoronto.ca, stevo@math.jussieu.fr"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada, and Universit\u00e9 Paris 7, CNRS \u2013 FRE 3233, 75251 Paris, France, E-mail:","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I185261750","https://openalex.org/I204730241"]},{"raw_affiliation_string":"Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada, and Universit\u00e9 Paris 7, CNRS \u2013 FRE 3233, 75251 Paris, France, E-mail/i: stevo@math.utoronto.ca, stevo@math.jussieu.fr","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I185261750","https://openalex.org/I204730241"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018265011"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I185261750","https://openalex.org/I204730241"],"apc_list":null,"apc_paid":null,"fwci":3.5264,"has_fulltext":true,"cited_by_count":29,"citation_normalized_percentile":{"value":0.93065918,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"17","issue":"1","first_page":"1","last_page":"72"},"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":0.9955999851226807,"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":0.9908000230789185,"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":0.9212363362312317},{"id":"https://openalex.org/keywords/dichotomy","display_name":"Dichotomy","score":0.8230799436569214},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5870327353477478},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.5759760737419128},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46690043807029724},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.45406150817871094},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.41533833742141724},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4009106159210205},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.3877023458480835},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.29922816157341003},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20554837584495544},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.16192084550857544},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.06303262710571289},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05518803000450134}],"concepts":[{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.9212363362312317},{"id":"https://openalex.org/C59462968","wikidata":"https://www.wikidata.org/wiki/Q10361123","display_name":"Dichotomy","level":2,"score":0.8230799436569214},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5870327353477478},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.5759760737419128},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46690043807029724},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.45406150817871094},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.41533833742141724},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4009106159210205},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.3877023458480835},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29922816157341003},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20554837584495544},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.16192084550857544},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.06303262710571289},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05518803000450134},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2178/bsl/1294186662","is_oa":true,"landing_page_url":"https://doi.org/10.2178/bsl/1294186662","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D1E79287F8D3E93B43955455930B4A7C/S1079898600000627a.pdf/div-class-title-combinatorial-dichotomies-in-set-theory-div.pdf","source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"The Bulletin of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.170.2444","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.170.2444","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.toronto.edu/%7Estevo/dichotomies4.pdf","raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.bsl/1294186662","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bsl/1294186662","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":{"id":"doi:10.2178/bsl/1294186662","is_oa":true,"landing_page_url":"https://doi.org/10.2178/bsl/1294186662","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D1E79287F8D3E93B43955455930B4A7C/S1079898600000627a.pdf/div-class-title-combinatorial-dichotomies-in-set-theory-div.pdf","source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"The Bulletin of Symbolic Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2065342370.pdf","grobid_xml":"https://content.openalex.org/works/W2065342370.grobid-xml"},"referenced_works_count":141,"referenced_works":["https://openalex.org/W70564106","https://openalex.org/W80350220","https://openalex.org/W191397503","https://openalex.org/W347715513","https://openalex.org/W568265359","https://openalex.org/W568866001","https://openalex.org/W612740589","https://openalex.org/W642652845","https://openalex.org/W806742853","https://openalex.org/W820565775","https://openalex.org/W834267236","https://openalex.org/W969915364","https://openalex.org/W1010521797","https://openalex.org/W1427302000","https://openalex.org/W1480159069","https://openalex.org/W1489871065","https://openalex.org/W1508043806","https://openalex.org/W1527476078","https://openalex.org/W1532059787","https://openalex.org/W1564080410","https://openalex.org/W1569878307","https://openalex.org/W1577853874","https://openalex.org/W1582222774","https://openalex.org/W1582291305","https://openalex.org/W1590716824","https://openalex.org/W1591627679","https://openalex.org/W1595022139","https://openalex.org/W1601878490","https://openalex.org/W1640652798","https://openalex.org/W1669528654","https://openalex.org/W1683522991","https://openalex.org/W1932818938","https://openalex.org/W1964920721","https://openalex.org/W1968053885","https://openalex.org/W1971010887","https://openalex.org/W1974966381","https://openalex.org/W1976490080","https://openalex.org/W1978262358","https://openalex.org/W1978413491","https://openalex.org/W1982184206","https://openalex.org/W1991014694","https://openalex.org/W1993569684","https://openalex.org/W1995217618","https://openalex.org/W1997553844","https://openalex.org/W1999287448","https://openalex.org/W2000037742","https://openalex.org/W2002685565","https://openalex.org/W2005772221","https://openalex.org/W2007083429","https://openalex.org/W2010359168","https://openalex.org/W2014748403","https://openalex.org/W2023241546","https://openalex.org/W2025774568","https://openalex.org/W2026196056","https://openalex.org/W2027648322","https://openalex.org/W2028336771","https://openalex.org/W2031855206","https://openalex.org/W2041358239","https://openalex.org/W2042427789","https://openalex.org/W2043270222","https://openalex.org/W2043313700","https://openalex.org/W2043487891","https://openalex.org/W2043717902","https://openalex.org/W2043782027","https://openalex.org/W2044935944","https://openalex.org/W2045418187","https://openalex.org/W2046445464","https://openalex.org/W2046660375","https://openalex.org/W2048750623","https://openalex.org/W2049220708","https://openalex.org/W2050504298","https://openalex.org/W2052846058","https://openalex.org/W2060319355","https://openalex.org/W2060403635","https://openalex.org/W2060532664","https://openalex.org/W2061391432","https://openalex.org/W2063123775","https://openalex.org/W2063927884","https://openalex.org/W2065348813","https://openalex.org/W2070702249","https://openalex.org/W2070957642","https://openalex.org/W2072022533","https://openalex.org/W2073081340","https://openalex.org/W2079026375","https://openalex.org/W2079152571","https://openalex.org/W2082458034","https://openalex.org/W2083949954","https://openalex.org/W2091169462","https://openalex.org/W2103936981","https://openalex.org/W2106941449","https://openalex.org/W2117873821","https://openalex.org/W2122005522","https://openalex.org/W2122092051","https://openalex.org/W2124054180","https://openalex.org/W2134581608","https://openalex.org/W2156505418","https://openalex.org/W2156672165","https://openalex.org/W2157996049","https://openalex.org/W2319297044","https://openalex.org/W2322797218","https://openalex.org/W2324578632","https://openalex.org/W2327445610","https://openalex.org/W2327567367","https://openalex.org/W2327679483","https://openalex.org/W2331307912","https://openalex.org/W2484259929","https://openalex.org/W2492799169","https://openalex.org/W2576738953","https://openalex.org/W2577011686","https://openalex.org/W2919539130","https://openalex.org/W2949873143","https://openalex.org/W2953753708","https://openalex.org/W2963762032","https://openalex.org/W2964133385","https://openalex.org/W3037467464","https://openalex.org/W3105725044","https://openalex.org/W4205248460","https://openalex.org/W4210359368","https://openalex.org/W4212769494","https://openalex.org/W4232053157","https://openalex.org/W4232141190","https://openalex.org/W4234476515","https://openalex.org/W4237640585","https://openalex.org/W4239353665","https://openalex.org/W4240551209","https://openalex.org/W4248490242","https://openalex.org/W4250254881","https://openalex.org/W4250699352","https://openalex.org/W4250747102","https://openalex.org/W4252338339","https://openalex.org/W4253897467","https://openalex.org/W4254807835","https://openalex.org/W4255035825","https://openalex.org/W4256522009","https://openalex.org/W6631865125","https://openalex.org/W6634792285","https://openalex.org/W6645636109","https://openalex.org/W6663835046","https://openalex.org/W6666837461","https://openalex.org/W6764767190","https://openalex.org/W7056227344"],"related_works":["https://openalex.org/W2100222222","https://openalex.org/W1982069151","https://openalex.org/W2256572025","https://openalex.org/W4303646992","https://openalex.org/W2952146172","https://openalex.org/W4300882518","https://openalex.org/W2068604232","https://openalex.org/W2092513686","https://openalex.org/W1986183533","https://openalex.org/W2185713319"],"abstract_inverted_index":{"Abstract":[0],"We":[1,68],"give":[2,69],"an":[3],"overview":[4],"of":[5,20,43,50,57,66],"a":[6],"research":[7,58],"line":[8,56],"concentrated":[9],"on":[10,32],"finding":[11],"to":[12,25,46,63],"which":[13,26],"extent":[14,27],"compactness":[15],"fails":[16],"at":[17],"the":[18,51],"level":[19],"first":[21],"uncountable":[22],"cardinal":[23],"and":[24,74],"it":[28],"could":[29],"be":[30],"recovered":[31],"some":[33,70,77],"other":[34,64],"perhaps":[35],"not":[36],"so":[37],"large":[38],"cardinal.":[39],"While":[40],"this":[41,55,73],"is":[42,59],"great":[44],"interest":[45],"set":[47],"theorists,":[48],"one":[49],"main":[52],"motivations":[53],"behind":[54],"in":[60],"its":[61],"applicability":[62],"areas":[65],"mathematics.":[67],"details":[71],"about":[72],"we":[75],"expose":[76],"possible":[78],"directions":[79],"for":[80],"further":[81],"research.":[82]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}
