{"id":"https://openalex.org/W2053384789","doi":"https://doi.org/10.1051/ita:2007008","title":"On the hierarchies of \u0394<sub>2</sub><sup>0</sup>-real numbers","display_name":"On the hierarchies of \u0394<sub>2</sub><sup>0</sup>-real numbers","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2053384789","doi":"https://doi.org/10.1051/ita:2007008","mag":"2053384789"},"language":"en","primary_location":{"id":"doi:10.1051/ita:2007008","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita:2007008","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X","2804-7346"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","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/A5102089636","display_name":"Xizhong Zheng","orcid":null},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]},{"id":"https://openalex.org/I4210094170","display_name":"Landesamt f\u00fcr Soziales und Versorgung des Landes Brandenburg","ror":"https://ror.org/00fzeeb88","country_code":"DE","type":"government","lineage":["https://openalex.org/I4210094170"]},{"id":"https://openalex.org/I4210143701","display_name":"Carl-Thiem-Klinikum Cottbus","ror":"https://ror.org/044fhy270","country_code":"DE","type":"healthcare","lineage":["https://openalex.org/I4210143701"]},{"id":"https://openalex.org/I51783024","display_name":"Brandenburg University of Technology Cottbus-Senftenberg","ror":"https://ror.org/02wxx3e24","country_code":"DE","type":"education","lineage":["https://openalex.org/I51783024"]}],"countries":["CN","DE"],"is_corresponding":true,"raw_author_name":"Xizhong Zheng","raw_affiliation_strings":["Department of Computer Science, Jiangsu University, Zhenjiang 212013, China","Theoretische Informatik, BTU Cottbus, 03044 Cottbus, Germany; zheng@tu-cottbus.de","Theoretische Informatik, BTU Cottbus, 03044 Cottbus, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Jiangsu University, Zhenjiang 212013, China","institution_ids":["https://openalex.org/I115592961"]},{"raw_affiliation_string":"Theoretische Informatik, BTU Cottbus, 03044 Cottbus, Germany; zheng@tu-cottbus.de","institution_ids":["https://openalex.org/I4210094170","https://openalex.org/I4210143701","https://openalex.org/I51783024"]},{"raw_affiliation_string":"Theoretische Informatik, BTU Cottbus, 03044 Cottbus, Germany","institution_ids":["https://openalex.org/I51783024"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5102089636"],"corresponding_institution_ids":["https://openalex.org/I115592961","https://openalex.org/I4210094170","https://openalex.org/I4210143701","https://openalex.org/I51783024"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12012572,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"41","issue":"1","first_page":"3","last_page":"25"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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":0.9760000109672546,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9690999984741211,"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/natural-number","display_name":"Natural number","score":0.6851990818977356},{"id":"https://openalex.org/keywords/real-number","display_name":"Real number","score":0.6216573119163513},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5961815118789673},{"id":"https://openalex.org/keywords/rational-number","display_name":"Rational number","score":0.5802124738693237},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5737756490707397},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.533818244934082},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47914260625839233},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4109411835670471},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3458067774772644},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.2691233456134796},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.06382763385772705}],"concepts":[{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.6851990818977356},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.6216573119163513},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5961815118789673},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.5802124738693237},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5737756490707397},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.533818244934082},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47914260625839233},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4109411835670471},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3458067774772644},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2691233456134796},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.06382763385772705}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1051/ita:2007008","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita:2007008","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X","2804-7346"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},{"id":"pmh:oai:numdam.org:ITA_2007__41_1_3_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ita:2007008/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.41999998688697815,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W623765668","https://openalex.org/W1518163798","https://openalex.org/W1545819195","https://openalex.org/W1552949294","https://openalex.org/W1555711402","https://openalex.org/W1577501449","https://openalex.org/W1604665829","https://openalex.org/W1964728647","https://openalex.org/W1975452830","https://openalex.org/W1985920135","https://openalex.org/W2007775665","https://openalex.org/W2008273724","https://openalex.org/W2022731279","https://openalex.org/W2037469541","https://openalex.org/W2037917663","https://openalex.org/W2059288245","https://openalex.org/W2066786168","https://openalex.org/W2077737783","https://openalex.org/W2087699091","https://openalex.org/W2093468014","https://openalex.org/W2097003126","https://openalex.org/W2118139375","https://openalex.org/W2123819323","https://openalex.org/W2126160338","https://openalex.org/W2132161762","https://openalex.org/W2155434681","https://openalex.org/W2162795121","https://openalex.org/W4231629838","https://openalex.org/W4232277851","https://openalex.org/W4234451284","https://openalex.org/W4241646449","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2626419576","https://openalex.org/W2527877093","https://openalex.org/W2594052908","https://openalex.org/W4321514130","https://openalex.org/W2508096977","https://openalex.org/W2601782347","https://openalex.org/W322881982","https://openalex.org/W1972495134","https://openalex.org/W2889631185","https://openalex.org/W4239203488"],"abstract_inverted_index":{"A":[0],"real":[1],"number":[2],"x":[3],"is":[4],"called":[5,33],"\u039420":[6,55],"if":[7],"its":[8],"binary":[9],"expansion":[10],"corresponds":[11],"to":[12,51,67],"a":[13],"\u039420-set":[14],"of":[15,24,27,47,54,70],"natural":[16],"numbers.":[17],"Such":[18],"reals":[19],"are":[20],"just":[21],"the":[22,40,74],"limits":[23],"computable":[25],"sequences":[26,41],"rational":[28],"numbers":[29],"and":[30,76],"hence":[31],"also":[32],"computably":[34],"approximable.":[35],"Depending":[36],"on":[37],"how":[38],"fast":[39],"converge,":[42],"\u039420-reals":[43],"have":[44],"different":[45],"levels":[46],"effectiveness.":[48],"This":[49],"leads":[50],"various":[52],"hierarchies":[53,71],"reals.":[56],"In":[57],"this":[58],"survey":[59],"paper":[60],"we":[61],"summarize":[62],"several":[63],"recent":[64],"developments":[65],"related":[66],"such":[68],"kind":[69],"shown":[72],"by":[73],"author":[75],"his":[77],"collaborators.":[78]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2016-06-24T00:00:00"}
