{"id":"https://openalex.org/W2161387988","doi":"https://doi.org/10.1142/s0219061303000285","title":"DEFINABILITY OF THE JUMP OPERATOR IN THE ENUMERATION DEGREES","display_name":"DEFINABILITY OF THE JUMP OPERATOR IN THE ENUMERATION DEGREES","publication_year":2003,"publication_date":"2003-11-01","ids":{"openalex":"https://openalex.org/W2161387988","doi":"https://doi.org/10.1142/s0219061303000285","mag":"2161387988"},"language":"en","primary_location":{"id":"doi:10.1142/s0219061303000285","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061303000285","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/A5052577470","display_name":"I. Sh. Kalimullin","orcid":"https://orcid.org/0000-0002-5931-3453"},"institutions":[{"id":"https://openalex.org/I21203515","display_name":"Kazan Federal University","ror":"https://ror.org/05256ym39","country_code":"RU","type":"education","lineage":["https://openalex.org/I21203515"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"I. Sh. KALIMULLIN","raw_affiliation_strings":["Kazan State University, Kazan, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kazan State University, Kazan, Russia","institution_ids":["https://openalex.org/I21203515"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052577470"],"corresponding_institution_ids":["https://openalex.org/I21203515"],"apc_list":null,"apc_paid":null,"fwci":0.364,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.65047507,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"03","issue":"02","first_page":"257","last_page":"267"},"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9976999759674072,"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/T11567","display_name":"semigroups and automata theory","score":0.9966999888420105,"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":0.8817229270935059},{"id":"https://openalex.org/keywords/semilattice","display_name":"Semilattice","score":0.8399277925491333},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.7623459696769714},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6214320659637451},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6189738512039185},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.597696840763092},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5586435198783875},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.42302268743515015},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41894739866256714},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06038889288902283},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05885028839111328}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8817229270935059},{"id":"https://openalex.org/C132170107","wikidata":"https://www.wikidata.org/wiki/Q834585","display_name":"Semilattice","level":3,"score":0.8399277925491333},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.7623459696769714},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6214320659637451},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6189738512039185},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.597696840763092},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5586435198783875},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42302268743515015},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41894739866256714},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06038889288902283},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05885028839111328},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219061303000285","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061303000285","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":[{"display_name":"Reduced inequalities","score":0.44999998807907104,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W334685031","https://openalex.org/W2017193571","https://openalex.org/W2037662783","https://openalex.org/W2047316241","https://openalex.org/W2113021297","https://openalex.org/W2113444807","https://openalex.org/W2905135108","https://openalex.org/W3092462891","https://openalex.org/W4232277851"],"related_works":["https://openalex.org/W2587400934","https://openalex.org/W2046025312","https://openalex.org/W3100498169","https://openalex.org/W1999567411","https://openalex.org/W2578985712","https://openalex.org/W1998108307","https://openalex.org/W2161387988","https://openalex.org/W2044231811","https://openalex.org/W4241241280","https://openalex.org/W2031344019"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"the":[3,8,16],"e-degree":[4],"0'":[5],"e":[6,28],"and":[7],"map":[9],"u":[10],"\u21a6":[11],"u'":[12],"are":[13],"definable":[14],"in":[15],"upper":[17],"semilattice":[18],"of":[19,24],"all":[20],"e-degrees.":[21],"The":[22],"class":[23],"total":[25],"e-degrees":[26],"\u22650'":[27],"is":[29],"also":[30],"definable.":[31]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
