{"id":"https://openalex.org/W2113874518","doi":"https://doi.org/10.1142/s0219061313500086","title":"BOREL EQUIVALENCE RELATIONS AND LASCAR STRONG TYPES","display_name":"BOREL EQUIVALENCE RELATIONS AND LASCAR STRONG TYPES","publication_year":2013,"publication_date":"2013-10-29","ids":{"openalex":"https://openalex.org/W2113874518","doi":"https://doi.org/10.1142/s0219061313500086","mag":"2113874518"},"language":"en","primary_location":{"id":"doi:10.1142/s0219061313500086","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061313500086","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/A5033122829","display_name":"Krzysztof Krupi\u0144ski","orcid":"https://orcid.org/0000-0002-2243-4411"},"institutions":[{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"education","lineage":["https://openalex.org/I219388962"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"KRZYSZTOF KRUPI\u0143SKI","raw_affiliation_strings":["Instytut Matematyczny, Uniwersytet Wroc\u0142awski, pl. Grunwaldzki 2/4, 50-384 Wroc\u0142aw, Poland","University of Wroclaw,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instytut Matematyczny, Uniwersytet Wroc\u0142awski, pl. Grunwaldzki 2/4, 50-384 Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I219388962"]},{"raw_affiliation_string":"University of Wroclaw,","institution_ids":["https://openalex.org/I219388962"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110147319","display_name":"Anand Pillay","orcid":"https://orcid.org/0000-0002-2471-4097"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"ANAND PILLAY","raw_affiliation_strings":["School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK","institution_ids":["https://openalex.org/I130828816"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012953076","display_name":"S\u0142awomir Solecki","orcid":"https://orcid.org/0000-0003-4152-1585"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S\u0141AWOMIR SOLECKI","raw_affiliation_strings":["Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL 61801, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL 61801, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5867,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.92165669,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"13","issue":"02","first_page":"1350008","last_page":"1350008"},"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":0.9817000031471252,"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":0.9796000123023987,"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/mathematics","display_name":"Mathematics","score":0.9018714427947998},{"id":"https://openalex.org/keywords/borel-equivalence-relation","display_name":"Borel equivalence relation","score":0.7841314077377319},{"id":"https://openalex.org/keywords/borel-hierarchy","display_name":"Borel hierarchy","score":0.6804463863372803},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.5860095620155334},{"id":"https://openalex.org/keywords/quotient-space","display_name":"Quotient space (topology)","score":0.5467263460159302},{"id":"https://openalex.org/keywords/descriptive-complexity-theory","display_name":"Descriptive complexity theory","score":0.543738842010498},{"id":"https://openalex.org/keywords/borel-set","display_name":"Borel set","score":0.5236401557922363},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.43659013509750366},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4346347153186798},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.4301779866218567},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.42123907804489136},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4129931926727295},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.30959033966064453},{"id":"https://openalex.org/keywords/borel-measure","display_name":"Borel measure","score":0.29578760266304016},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.11506175994873047}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9018714427947998},{"id":"https://openalex.org/C5278979","wikidata":"https://www.wikidata.org/wiki/Q4944905","display_name":"Borel equivalence relation","level":4,"score":0.7841314077377319},{"id":"https://openalex.org/C25942563","wikidata":"https://www.wikidata.org/wiki/Q893487","display_name":"Borel hierarchy","level":4,"score":0.6804463863372803},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.5860095620155334},{"id":"https://openalex.org/C40753290","wikidata":"https://www.wikidata.org/wiki/Q1139111","display_name":"Quotient space (topology)","level":3,"score":0.5467263460159302},{"id":"https://openalex.org/C133142742","wikidata":"https://www.wikidata.org/wiki/Q1200755","display_name":"Descriptive complexity theory","level":3,"score":0.543738842010498},{"id":"https://openalex.org/C39952206","wikidata":"https://www.wikidata.org/wiki/Q21086747","display_name":"Borel set","level":2,"score":0.5236401557922363},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43659013509750366},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4346347153186798},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.4301779866218567},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.42123907804489136},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4129931926727295},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.30959033966064453},{"id":"https://openalex.org/C166758865","wikidata":"https://www.wikidata.org/wiki/Q892585","display_name":"Borel measure","level":3,"score":0.29578760266304016},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.11506175994873047},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219061313500086","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061313500086","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":[{"id":"https://openalex.org/G5940767488","display_name":null,"funder_award_id":"EP/I002294/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W633186680","https://openalex.org/W635392658","https://openalex.org/W1214187494","https://openalex.org/W1539382740","https://openalex.org/W1602868010","https://openalex.org/W1835487350","https://openalex.org/W1842991113","https://openalex.org/W1979182440","https://openalex.org/W1989573501","https://openalex.org/W1990678597","https://openalex.org/W1999410161","https://openalex.org/W2019185145","https://openalex.org/W2019357210","https://openalex.org/W2024986251","https://openalex.org/W2079152571","https://openalex.org/W2093835911","https://openalex.org/W2105780736","https://openalex.org/W2114132752","https://openalex.org/W2138593475","https://openalex.org/W2157886454","https://openalex.org/W2158457721","https://openalex.org/W2472703513","https://openalex.org/W3100318695"],"related_works":["https://openalex.org/W1491956444","https://openalex.org/W2031042539","https://openalex.org/W2122677906","https://openalex.org/W2080776953","https://openalex.org/W4299887575","https://openalex.org/W2255570240","https://openalex.org/W2140891656","https://openalex.org/W2021474232","https://openalex.org/W1627906788","https://openalex.org/W2113874518"],"abstract_inverted_index":{"The":[0,36,81,103,137,189],"\"space\"":[1],"of":[2,43,63,72,75,77,89,96,109,139,144,147,149,170,183,199,213,225],"Lascar":[3,44,58,150],"strong":[4,45,151],"types,":[5,46],"on":[6,155],"some":[7,97,124,252],"sort":[8],"and":[9,53,113,117,133,165,208,216,228,238,244],"relative":[10],"to":[11,39,84,106,231],"a":[12,21,140,184],"given":[13],"complete":[14],"theory":[15,74],"T,":[16,64],"is":[17,38,83,105,195],"in":[18,33,156,205,233,241,251],"general":[19],"not":[20],"compact":[22],"Hausdorff":[23],"topological":[24],"space.":[25],"We":[26,121],"have":[27,65],"at":[28],"least":[29],"three":[30],"(modest)":[31],"aims":[32],"this":[34,193],"paper.":[35],"first":[37,171,181],"show":[40],"that":[41,100],"spaces":[42,52,148],"as":[47,49,56,93,95],"well":[48,94],"other":[50],"related":[51,118],"objects":[54],"such":[55],"the":[57,70,73,86,90,126,145,157,180,197,239],"group":[59,253],"Gal":[60],"L":[61],"(T)":[62],"well-defined":[66],"Borel":[67,78,87],"cardinalities":[68,88],"(in":[69],"sense":[71],"complexity":[76,146],"equivalence":[79],"relations).":[80],"second":[82],"compute":[85],"known":[91],"examples":[92,99,201],"new":[98,200],"we":[101],"give.":[102],"third":[104],"explore":[107],"notions":[108],"definable":[110,203,214,226],"map,":[111],"embedding,":[112],"isomorphism,":[114],"between":[115],"these":[116],"quotient":[119],"objects.":[120],"also":[122],"make":[123],"conjectures,":[125],"main":[127],"one":[128],"being":[129],"roughly":[130],"\"smooth":[131],"if":[132,135],"only":[134],"trivial\".":[136],"possibility":[138],"descriptive":[141],"set-theoretic":[142],"account":[143],"types":[152],"was":[153,187],"touched":[154],"paper":[158,194],"[E.":[159],"Casanovas,":[160],"D.":[161],"Lascar,":[162],"A.":[163,209],"Pillay":[164],"M.":[166],"Ziegler,":[167],"Galois":[168],"groups":[169,215,227],"order":[172],"theories,":[173],"J.":[174],"Math.":[175],"Logic1":[176],"(2001)":[177],"305\u2013319],":[178],"where":[179],"example":[182],"\"non-G-compact":[185],"theory\"":[186],"given.":[188],"motivation":[190],"for":[191],"writing":[192],"partly":[196],"discovery":[198],"via":[202],"groups,":[204],"[A.":[206],"Conversano":[207],"Pillay,":[210],"Connected":[211,223],"components":[212,224,250],"o-minimality":[217,229],"I,":[218],"Adv.":[219],"Math.231":[220],"(2012)":[221],"605\u2013623;":[222],"II,":[230],"appear":[232],"Ann.":[234],"Pure":[235],"Appl.":[236],"Logic]":[237],"generalizations":[240],"[J.":[242],"Gismatullin":[243],"K.":[245],"Krupi\u0144ski,":[246],"On":[247],"model-theoretic":[248],"connected":[249],"extensions,":[254],"preprint":[255],"(2012),":[256],"arXiv:1201.5221v1].":[257]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}