{"id":"https://openalex.org/W3216020637","doi":"https://doi.org/10.1002/malq.202100004","title":"Normalizing notations in the Ershov hierarchy","display_name":"Normalizing notations in the Ershov hierarchy","publication_year":2021,"publication_date":"2021-11-01","ids":{"openalex":"https://openalex.org/W3216020637","doi":"https://doi.org/10.1002/malq.202100004","mag":"3216020637"},"language":"en","primary_location":{"id":"doi:10.1002/malq.202100004","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.202100004","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","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/A5055034888","display_name":"Cheng Peng","orcid":"https://orcid.org/0000-0002-8342-1964"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Cheng Peng","raw_affiliation_strings":["School of Mathematical Sciences Nankai University Tianjin City 300071 China","School of Mathematical Sciences, Nankai University, Tianjin City, 300071 China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences Nankai University Tianjin City 300071 China","institution_ids":["https://openalex.org/I205237279"]},{"raw_affiliation_string":"School of Mathematical Sciences, Nankai University, Tianjin City, 300071 China","institution_ids":["https://openalex.org/I205237279"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5055034888"],"corresponding_institution_ids":["https://openalex.org/I205237279"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21259421,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"67","issue":"4","first_page":"506","last_page":"513"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.9742000102996826,"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":0.9585999846458435,"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/mathematics","display_name":"Mathematics","score":0.7568001747131348},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.6353651881217957},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.6274647116661072},{"id":"https://openalex.org/keywords/lift","display_name":"Lift (data mining)","score":0.5238670706748962},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4652121365070343},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3543357849121094},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3312087059020996},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2711421847343445},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18735677003860474},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.13566794991493225},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.07215458154678345},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.05423042178153992}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7568001747131348},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6353651881217957},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6274647116661072},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.5238670706748962},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4652121365070343},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3543357849121094},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3312087059020996},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2711421847343445},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18735677003860474},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.13566794991493225},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.07215458154678345},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.05423042178153992},{"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},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.202100004","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.202100004","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G983743152","display_name":null,"funder_award_id":"11725103","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W2005798738","https://openalex.org/W2007016528","https://openalex.org/W2037320888","https://openalex.org/W2037416374","https://openalex.org/W2060218907","https://openalex.org/W2169764068","https://openalex.org/W2324179631","https://openalex.org/W2493019513","https://openalex.org/W2905135108","https://openalex.org/W3114679342"],"related_works":["https://openalex.org/W1515801737","https://openalex.org/W2010890875","https://openalex.org/W2020478166","https://openalex.org/W2511589825","https://openalex.org/W2768956924","https://openalex.org/W3050182513","https://openalex.org/W2012308389","https://openalex.org/W2322102914","https://openalex.org/W2580864378","https://openalex.org/W2086179181"],"abstract_inverted_index":{"Abstract":[0],"The":[1,70],"Turing":[2,26],"degrees":[3,27,96],"of":[4,7,25,28,35,60,72,101],"infinite":[5,29,99],"levels":[6,30,40,85,100],"the":[8,23,33,39,58,73,78,87,94,98,102],"Ershov":[9,88,103],"hierarchy":[10],"were":[11],"studied":[12],"by":[13],"Liu":[14],"and":[15,31,63,77],"Peng":[16],"[8].":[17],"In":[18,45],"this":[19],"paper,":[20],"we":[21,48,91],"continue":[22],"study":[24,34],"lift":[32],"density":[36,75],"property":[37],"to":[38],"beyond":[41],"\u03c9":[42],"2":[43],".":[44],"doing":[46],"so,":[47],"rely":[49],"on":[50],"notations":[51,62,66],"with":[52],"some":[53],"nice":[54],"properties.":[55],"We":[56],"introduce":[57],"concept":[59],"normalizing":[61,65],"generate":[64],"for":[67,83],"higher":[68,84],"levels.":[69],"generalizations":[71],"weak":[74],"theorem":[76,80],"nondensity":[79],"are":[81],"proved":[82],"in":[86,97],"hierarchy.":[89,104],"Furthermore,":[90],"also":[92],"investigate":[93],"minimal":[95]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
