{"id":"https://openalex.org/W2169114697","doi":"https://doi.org/10.1017/s0022481200041104","title":"Recursively enumerable sets modulo iterated jumps and extensions of Arslanov's completeness criterion","display_name":"Recursively enumerable sets modulo iterated jumps and extensions of Arslanov's completeness criterion","publication_year":1989,"publication_date":"1989-12-01","ids":{"openalex":"https://openalex.org/W2169114697","doi":"https://doi.org/10.1017/s0022481200041104","mag":"2169114697"},"language":"en","primary_location":{"id":"doi:10.1017/s0022481200041104","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0022481200041104","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/A5037418038","display_name":"C. G. Jockusch","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. G. Jockusch","raw_affiliation_strings":["Department of Mathematics, University of Illinois, Urbana, Illinois 61801"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Illinois, Urbana, Illinois 61801","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003510558","display_name":"M. Lerman","orcid":null},"institutions":[{"id":"https://openalex.org/I140172145","display_name":"University of Connecticut","ror":"https://ror.org/02der9h97","country_code":"US","type":"education","lineage":["https://openalex.org/I140172145"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Lerman","raw_affiliation_strings":["Department of Mathematics, University of Connecticut, Storrs, Connecticut 06268"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Connecticut, Storrs, Connecticut 06268","institution_ids":["https://openalex.org/I140172145"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023422267","display_name":"Robert I. Soare","orcid":null},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R. I. Soare","raw_affiliation_strings":["Department of Mathematics, University of Chicago, Chicago, Illinois 60637"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Chicago, Chicago, Illinois 60637","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000834004","display_name":"R. M. Solovay","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R. M. Solovay","raw_affiliation_strings":["Department of Mathematics, University of California, Berkeley, California 94720"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Berkeley, California 94720","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9172,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.87166003,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"54","issue":"4","first_page":"1288","last_page":"1323"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9868999719619751,"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":0.811522901058197},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.7025812864303589},{"id":"https://openalex.org/keywords/recursively-enumerable-language","display_name":"Recursively enumerable language","score":0.6909220814704895},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.6715132594108582},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.626409649848938},{"id":"https://openalex.org/keywords/recursively-enumerable-set","display_name":"Recursively enumerable set","score":0.6037662029266357},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.6028959155082703},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5262757539749146},{"id":"https://openalex.org/keywords/equivalence-class","display_name":"Equivalence class (music)","score":0.4461890459060669},{"id":"https://openalex.org/keywords/least-fixed-point","display_name":"Least fixed point","score":0.4354649484157562},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4185047447681427},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.4110203683376312},{"id":"https://openalex.org/keywords/brouwer-fixed-point-theorem","display_name":"Brouwer fixed-point theorem","score":0.2935330271720886},{"id":"https://openalex.org/keywords/schauder-fixed-point-theorem","display_name":"Schauder fixed point theorem","score":0.26883864402770996},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08079653978347778}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.811522901058197},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.7025812864303589},{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.6909220814704895},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.6715132594108582},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.626409649848938},{"id":"https://openalex.org/C52703633","wikidata":"https://www.wikidata.org/wiki/Q676835","display_name":"Recursively enumerable set","level":3,"score":0.6037662029266357},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.6028959155082703},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5262757539749146},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.4461890459060669},{"id":"https://openalex.org/C27333817","wikidata":"https://www.wikidata.org/wiki/Q6134913","display_name":"Least fixed point","level":5,"score":0.4354649484157562},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4185047447681427},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.4110203683376312},{"id":"https://openalex.org/C146147875","wikidata":"https://www.wikidata.org/wiki/Q1144897","display_name":"Brouwer fixed-point theorem","level":3,"score":0.2935330271720886},{"id":"https://openalex.org/C28642324","wikidata":"https://www.wikidata.org/wiki/Q656176","display_name":"Schauder fixed point theorem","level":4,"score":0.26883864402770996},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08079653978347778}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0022481200041104","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0022481200041104","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/1183743101","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183743101","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W10794601","https://openalex.org/W73737415","https://openalex.org/W1480985349","https://openalex.org/W1514415888","https://openalex.org/W1554860413","https://openalex.org/W1556269025","https://openalex.org/W1556584770","https://openalex.org/W1566235828","https://openalex.org/W2029823283","https://openalex.org/W2037469541","https://openalex.org/W2055180636","https://openalex.org/W2083623332","https://openalex.org/W2101746971","https://openalex.org/W2117832390","https://openalex.org/W2492513299","https://openalex.org/W2494466741","https://openalex.org/W2530006810","https://openalex.org/W2905135108","https://openalex.org/W2991196623","https://openalex.org/W3133279294","https://openalex.org/W4231202900","https://openalex.org/W4232277851","https://openalex.org/W4246804796","https://openalex.org/W6603067411","https://openalex.org/W6828398953"],"related_works":["https://openalex.org/W2037833610","https://openalex.org/W1972481159","https://openalex.org/W1973052363","https://openalex.org/W2000487993","https://openalex.org/W2094468224","https://openalex.org/W1980641386","https://openalex.org/W2132512348","https://openalex.org/W2089792255","https://openalex.org/W1555094413","https://openalex.org/W2117594216"],"abstract_inverted_index":{"Let":[0,159],"W":[1,44,47],"e":[2,5,32,45,50],"be":[3,131,161],"the":[4,41,62,76,95,98,107,121,149],"th":[6],"recursively":[7,88],"enumerable":[8,89],"(r.e.)":[9],"set":[10],"in":[11,40,75,133,151,183],"a":[12,35,145,179],"standard":[13],"enumeration.":[14],"The":[15],"fixed":[16,36,68,73,81,104,187],"point":[17,37,93,188],"form":[18],"of":[19,38,64,97,100,126,148,153],"Kleene's":[20],"recursion":[21],"theorem":[22],"asserts":[23],"that":[24,43],"for":[25,94],"every":[26],"recursive":[27,182],"function":[28,180],"f":[29,39,48,181],"there":[30,177],"exists":[31],"which":[33],"is":[34,59,106,167,178],"sense":[42,78],"=":[46],"(":[49,169],")":[51],".":[52,189],"In":[53],"this":[54,127,154],"paper":[55],"our":[56],"main":[57],"concern":[58],"to":[60,111],"study":[61],"degrees":[63,99],"functions":[65,101],"with":[66,185],"no":[67,186],"points.":[69],"We":[70],"consider":[71],"both":[72],"points":[74,82,105],"strict":[77],"above":[79],"and":[80,118,137,141],"modulo":[83],"various":[84],"equivalence":[85],"relations":[86],"on":[87],"sets.":[90],"Our":[91],"starting":[92],"investigation":[96],"without":[102],"(strict)":[103],"following":[108],"result":[109,128],"due":[110],"M.":[112,113],"Arslanov":[114,122],"[A1,":[115],"Theorem":[116,135,156],"1]":[117],"known":[119],"as":[120],"completeness":[123],"criterion.":[124],"Proofs":[125],"may":[129],"also":[130],"found":[132],"[So1,":[134],"1.3]":[136],"[So2,":[138],"Chapter":[139],"12],":[140],"we":[142],"will":[143],"give":[144],"game":[146],"version":[147],"proof":[150],"\u00a75":[152],"paper.":[155],"1.1":[157],"(Arslanov).":[158],"A":[160,166,171,184],"an":[162],"r.e.":[163],"set.":[164],"Then":[165],"complete":[168],"i.e.":[170],"has":[172],"degree":[173],"0":[174],"\u2032)":[175],"iff":[176]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}