{"id":"https://openalex.org/W2042456363","doi":"https://doi.org/10.2307/2274645","title":"On the quasi-ordering of Borel linear orders under embeddability","display_name":"On the quasi-ordering of Borel linear orders under embeddability","publication_year":1990,"publication_date":"1990-06-01","ids":{"openalex":"https://openalex.org/W2042456363","doi":"https://doi.org/10.2307/2274645","mag":"2042456363"},"language":"en","primary_location":{"id":"doi:10.2307/2274645","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274645","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/A5081586917","display_name":"Alain Louveau","orcid":null},"institutions":[{"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"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I48825208","display_name":"Universit\u00e9 Paris 8","ror":"https://ror.org/04wez5e68","country_code":"FR","type":"education","lineage":["https://openalex.org/I48825208"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alain Louveau","raw_affiliation_strings":["\u00c9quipe D'Analyse, Universit\u00e9 Paris-VI, 75252 Paris, France","universit\u00e9 Paris VI"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9quipe D'Analyse, Universit\u00e9 Paris-VI, 75252 Paris, France","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I48825208"]},{"raw_affiliation_string":"universit\u00e9 Paris VI","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I39804081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111607472","display_name":"Jean Saint-Raymond","orcid":null},"institutions":[{"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"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I48825208","display_name":"Universit\u00e9 Paris 8","ror":"https://ror.org/04wez5e68","country_code":"FR","type":"education","lineage":["https://openalex.org/I48825208"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean Saint-Raymond","raw_affiliation_strings":["\u00c9quipe D'Analyse, Universit\u00e9 Paris-VI, 75252 Paris, France","universit\u00e9 Paris VI"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9quipe D'Analyse, Universit\u00e9 Paris-VI, 75252 Paris, France","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I48825208"]},{"raw_affiliation_string":"universit\u00e9 Paris VI","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I39804081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1826,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.8985971,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"55","issue":"2","first_page":"537","last_page":"560"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9970999956130981,"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":0.9970999956130981,"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":0.9786999821662903,"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"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.972000002861023,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/determinacy","display_name":"Determinacy","score":0.9531089663505554},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8239461183547974},{"id":"https://openalex.org/keywords/lexicographical-order","display_name":"Lexicographical order","score":0.7620379328727722},{"id":"https://openalex.org/keywords/borel-equivalence-relation","display_name":"Borel equivalence relation","score":0.5455727577209473},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5257735252380371},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4731130301952362},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.47223779559135437},{"id":"https://openalex.org/keywords/borel-set","display_name":"Borel set","score":0.4571812152862549},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41843026876449585},{"id":"https://openalex.org/keywords/borel-measure","display_name":"Borel measure","score":0.32897770404815674},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16175192594528198},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.06197503209114075},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06176069378852844}],"concepts":[{"id":"https://openalex.org/C58468513","wikidata":"https://www.wikidata.org/wiki/Q1201165","display_name":"Determinacy","level":2,"score":0.9531089663505554},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8239461183547974},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.7620379328727722},{"id":"https://openalex.org/C5278979","wikidata":"https://www.wikidata.org/wiki/Q4944905","display_name":"Borel equivalence relation","level":4,"score":0.5455727577209473},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5257735252380371},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4731130301952362},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47223779559135437},{"id":"https://openalex.org/C39952206","wikidata":"https://www.wikidata.org/wiki/Q21086747","display_name":"Borel set","level":2,"score":0.4571812152862549},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41843026876449585},{"id":"https://openalex.org/C166758865","wikidata":"https://www.wikidata.org/wiki/Q892585","display_name":"Borel measure","level":3,"score":0.32897770404815674},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16175192594528198},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.06197503209114075},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06176069378852844},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2274645","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274645","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/1183743312","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183743312","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W177387391","https://openalex.org/W586883305","https://openalex.org/W1985409003","https://openalex.org/W2014244506","https://openalex.org/W2094635717","https://openalex.org/W2138899395","https://openalex.org/W2163841074","https://openalex.org/W2316932045","https://openalex.org/W4206193192","https://openalex.org/W4232141190","https://openalex.org/W4239860664"],"related_works":["https://openalex.org/W1491956444","https://openalex.org/W2031042539","https://openalex.org/W4243177823","https://openalex.org/W4233502995","https://openalex.org/W1516336919","https://openalex.org/W4299887575","https://openalex.org/W2037769602","https://openalex.org/W3146364253","https://openalex.org/W2058759841","https://openalex.org/W2201015916"],"abstract_inverted_index":{"Abstract":[0],"We":[1,19],"provide":[2],"partial":[3],"answers":[4],"to":[5],"the":[6,10,25,39,76],"following":[7],"problem:":[8],"Is":[9],"class":[11],"of":[12],"Borel":[13,29,43,61],"linear":[14],"orders":[15,30,44,62],"well-quasi-ordered":[16],"under":[17],"embeddability?":[18],"show":[20],"that":[21],"it":[22,56],"is":[23],"indeed":[24],"case":[26],"for":[27,60,75],"those":[28],"which":[31],"are":[32],"embeddable":[33,45,63],"in":[34,46,53,64],"R":[35,47,66],"\u03c9":[36],",":[37,49,68],"with":[38],"lexicographic":[40],"ordering.":[41],"For":[42],"2":[48],"our":[50],"proof":[51],"works":[52],"ZFC,":[54],"but":[55],"uses":[57],"projective":[58],"determinacy":[59,74],"some":[65],"n":[67,69],"&lt;":[70],"\u03c9,":[71],"and":[72],"hyperprojective":[73],"general":[77],"case.":[78]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
