{"id":"https://openalex.org/W2964127634","doi":"https://doi.org/10.1142/s0219061319500090","title":"Ordinal definability and combinatorics of equivalence relations","display_name":"Ordinal definability and combinatorics of equivalence relations","publication_year":2019,"publication_date":"2019-03-03","ids":{"openalex":"https://openalex.org/W2964127634","doi":"https://doi.org/10.1142/s0219061319500090","mag":"2964127634"},"language":"en","primary_location":{"id":"doi:10.1142/s0219061319500090","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061319500090","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical 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/A5016918393","display_name":"William Chan","orcid":"https://orcid.org/0000-0002-0661-1764"},"institutions":[{"id":"https://openalex.org/I123534392","display_name":"University of North Texas","ror":"https://ror.org/00v97ad02","country_code":"US","type":"education","lineage":["https://openalex.org/I123534392"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"William Chan","raw_affiliation_strings":["Department of Mathematics, University of North Texas, Denton, 76203 TX, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of North Texas, Denton, 76203 TX, USA","institution_ids":["https://openalex.org/I123534392"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016918393"],"corresponding_institution_ids":["https://openalex.org/I123534392"],"apc_list":null,"apc_paid":null,"fwci":2.685,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.9015237,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"19","issue":"02","first_page":"1950009","last_page":"1950009"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9772999882698059,"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":0.9772999882698059,"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/T11567","display_name":"semigroups and automata theory","score":0.975600004196167,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9555000066757202,"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":0.6735602021217346},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.5743824243545532},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5230951309204102},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.49424317479133606},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.463552862405777}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6735602021217346},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.5743824243545532},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5230951309204102},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.49424317479133606},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.463552862405777}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219061319500090","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061319500090","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Logic","raw_type":"journal-article"}],"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/W572278001","https://openalex.org/W635392658","https://openalex.org/W803471959","https://openalex.org/W1956305101","https://openalex.org/W2033288360","https://openalex.org/W2049795191","https://openalex.org/W2063046819","https://openalex.org/W2080112151","https://openalex.org/W2514887056","https://openalex.org/W2963332506","https://openalex.org/W3105870430","https://openalex.org/W4239969954","https://openalex.org/W4302047427"],"related_works":["https://openalex.org/W2063982045","https://openalex.org/W2150808137","https://openalex.org/W2001378190","https://openalex.org/W2026895631","https://openalex.org/W2061247757","https://openalex.org/W3186647487","https://openalex.org/W2582220712","https://openalex.org/W2093229750","https://openalex.org/W2964127634","https://openalex.org/W285280088"],"abstract_inverted_index":{"Assume":[0],"[Formula:":[1,5,10,17,20,38,43,47,53,58,64,75,83,87,94,101,106,114,121,124,127,132,138,147,153,157,163,167],"see":[2,6,11,18,21,39,44,48,54,59,65,76,84,88,95,102,107,115,122,125,128,133,139,148,154,158,164,168],"text].":[3,19,126,169],"Let":[4],"text]":[7,12,22,40,45,55,60,66,77,89,96,103,116,129,134,140,155,159,165],"be":[8],"a":[9,57,91,112],"equivalence":[13,27,61],"relation":[14,62,92],"coded":[15],"in":[16,70,160],"has":[23],"an":[24,105,142,152],"ordinal":[25,31],"definable":[26,32],"class":[28],"without":[29],"any":[30],"elements":[33],"if":[34,37],"and":[35,166],"only":[36],"is":[41,56,68,90,104,111,135,141,151],"unpinned.":[42],"proves":[46,130],"text]-class":[49],"section":[50,100],"uniformization":[51],"when":[52],"on":[63,93],"which":[67,81],"pinned":[69],"every":[71,145],"transitive":[72],"model":[73],"of":[74],"containing":[78],"the":[79],"real":[80],"codes":[82],"text]:":[85],"Suppose":[86],"such":[97,117],"that":[98,118,131],"each":[99],"text]-class,":[108],"then":[109],"there":[110,150],"function":[113,146],"for":[119],"all":[120],"text],":[123,149],"J\u00f3nsson":[136],"whenever":[137],"ordinal:":[143],"For":[144],"with":[156,162],"bijection":[161]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}