{"id":"https://openalex.org/W85778761","doi":"https://doi.org/10.1007/3-540-63165-8_162","title":"The Wadge-Wagner hierarchy of \u03c9-rational sets","display_name":"The Wadge-Wagner hierarchy of \u03c9-rational sets","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W85778761","doi":"https://doi.org/10.1007/3-540-63165-8_162","mag":"85778761"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-63165-8_162","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-63165-8_162","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5025290597","display_name":"Olivier Carton","orcid":"https://orcid.org/0000-0002-2728-6534"},"institutions":[{"id":"https://openalex.org/I4210152518","display_name":"Laboratoire d'Informatique Gaspard-Monge","ror":"https://ror.org/04t50yk91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210145102","https://openalex.org/I4210152518","https://openalex.org/I4210154111","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Olivier Carton","raw_affiliation_strings":["Institut Gaspard Monge, Universit\u00e9 de Marne-la-vall\u00e9e, 93166, Noisy le Grand, France","Universit\u00e9 de Marne-la-Vall\u00e9e"],"affiliations":[{"raw_affiliation_string":"Institut Gaspard Monge, Universit\u00e9 de Marne-la-vall\u00e9e, 93166, Noisy le Grand, France","institution_ids":["https://openalex.org/I4210152518"]},{"raw_affiliation_string":"Universit\u00e9 de Marne-la-Vall\u00e9e","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5105510505","display_name":"Dominique Perrin","orcid":"https://orcid.org/0000-0003-4036-141X"},"institutions":[{"id":"https://openalex.org/I4210152518","display_name":"Laboratoire d'Informatique Gaspard-Monge","ror":"https://ror.org/04t50yk91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210145102","https://openalex.org/I4210152518","https://openalex.org/I4210154111","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Dominique Perrin","raw_affiliation_strings":["Institut Gaspard Monge, Universit\u00e9 de Marne-la-vall\u00e9e, 93166, Noisy le Grand, France","Universit\u00e9 de Marne-la-Vall\u00e9e"],"affiliations":[{"raw_affiliation_string":"Institut Gaspard Monge, Universit\u00e9 de Marne-la-vall\u00e9e, 93166, Noisy le Grand, France","institution_ids":["https://openalex.org/I4210152518"]},{"raw_affiliation_string":"Universit\u00e9 de Marne-la-Vall\u00e9e","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025290597"],"corresponding_institution_ids":["https://openalex.org/I4210152518"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.5157,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.60701754,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"17","last_page":"35"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9976999759674072,"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"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9976999759674072,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9975000023841858,"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/T11567","display_name":"semigroups and automata theory","score":0.9921000003814697,"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/hierarchy","display_name":"Hierarchy","score":0.8488768339157104},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7097948789596558},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.5237833857536316},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5021893978118896},{"id":"https://openalex.org/keywords/analytical-hierarchy","display_name":"Analytical hierarchy","score":0.4540357291698456},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4496295750141144},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36056995391845703},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.35969728231430054},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33546435832977295},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.29753512144088745},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.20252621173858643},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.17478948831558228},{"id":"https://openalex.org/keywords/analytic-hierarchy-process","display_name":"Analytic hierarchy process","score":0.15860620141029358},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1369624137878418}],"concepts":[{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.8488768339157104},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7097948789596558},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.5237833857536316},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5021893978118896},{"id":"https://openalex.org/C176053320","wikidata":"https://www.wikidata.org/wiki/Q2878515","display_name":"Analytical hierarchy","level":3,"score":0.4540357291698456},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4496295750141144},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36056995391845703},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35969728231430054},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33546435832977295},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29753512144088745},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.20252621173858643},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.17478948831558228},{"id":"https://openalex.org/C87345402","wikidata":"https://www.wikidata.org/wiki/Q485202","display_name":"Analytic hierarchy process","level":2,"score":0.15860620141029358},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1369624137878418},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-63165-8_162","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-63165-8_162","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5600000023841858}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W3130855","https://openalex.org/W21817812","https://openalex.org/W117768600","https://openalex.org/W164886591","https://openalex.org/W177787971","https://openalex.org/W183585617","https://openalex.org/W204701247","https://openalex.org/W1487875360","https://openalex.org/W1539382740","https://openalex.org/W1560050980","https://openalex.org/W1565611252","https://openalex.org/W1600140231","https://openalex.org/W1859852581","https://openalex.org/W1974774490","https://openalex.org/W1977229748","https://openalex.org/W2003940577","https://openalex.org/W2019932899","https://openalex.org/W2025480213","https://openalex.org/W2028004422","https://openalex.org/W2057300641","https://openalex.org/W2072058455","https://openalex.org/W2082036629","https://openalex.org/W4206252072"],"related_works":["https://openalex.org/W2095175072","https://openalex.org/W2008977977","https://openalex.org/W1575303034","https://openalex.org/W2590361123","https://openalex.org/W2040673363","https://openalex.org/W1996184580","https://openalex.org/W1522180487","https://openalex.org/W4206650230","https://openalex.org/W2292703908","https://openalex.org/W1969386550"],"abstract_inverted_index":null,"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}