{"id":"https://openalex.org/W2083502326","doi":"https://doi.org/10.2307/2274854","title":"A limit on relative genericity in the recursively enumerable sets","display_name":"A limit on relative genericity in the recursively enumerable sets","publication_year":1989,"publication_date":"1989-06-01","ids":{"openalex":"https://openalex.org/W2083502326","doi":"https://doi.org/10.2307/2274854","mag":"2083502326"},"language":"en","primary_location":{"id":"doi:10.2307/2274854","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274854","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/A5032435178","display_name":"Steffen Lempp","orcid":"https://orcid.org/0000-0002-2958-4017"},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Steffen Lempp","raw_affiliation_strings":["Department of Mathematics, Yale University, New Haven, Connecticut 06520","Yale University  ;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yale University, New Haven, Connecticut 06520","institution_ids":["https://openalex.org/I32971472"]},{"raw_affiliation_string":"Yale University  ;","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056375116","display_name":"Theodore A. Slaman","orcid":"https://orcid.org/0000-0002-1719-2630"},"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":"Theodore A. Slaman","raw_affiliation_strings":["Department of Mathematics, University of Chicago, Chicago, Illinois 60637","University-of Chicago"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Chicago, Chicago, Illinois 60637","institution_ids":["https://openalex.org/I40347166"]},{"raw_affiliation_string":"University-of Chicago","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032435178"],"corresponding_institution_ids":["https://openalex.org/I32971472"],"apc_list":null,"apc_paid":null,"fwci":0.4789,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.65547653,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"54","issue":"2","first_page":"376","last_page":"395"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":1.0,"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":1.0,"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":0.9876000285148621,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9746000170707703,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/recursively-enumerable-language","display_name":"Recursively enumerable language","score":0.9590826034545898},{"id":"https://openalex.org/keywords/recursively-enumerable-set","display_name":"Recursively enumerable set","score":0.7506921887397766},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.6267334222793579},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6158843040466309},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5993717908859253},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5748288035392761},{"id":"https://openalex.org/keywords/maximal-set","display_name":"Maximal set","score":0.5640806555747986},{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.5613967776298523},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5337544083595276},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4972827732563019},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4875616431236267},{"id":"https://openalex.org/keywords/turing-machine","display_name":"Turing machine","score":0.45759138464927673},{"id":"https://openalex.org/keywords/description-number","display_name":"Description number","score":0.4418129324913025},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3112080991268158},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.280345618724823},{"id":"https://openalex.org/keywords/universal-turing-machine","display_name":"Universal Turing machine","score":0.083354651927948}],"concepts":[{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.9590826034545898},{"id":"https://openalex.org/C52703633","wikidata":"https://www.wikidata.org/wiki/Q676835","display_name":"Recursively enumerable set","level":3,"score":0.7506921887397766},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.6267334222793579},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6158843040466309},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5993717908859253},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5748288035392761},{"id":"https://openalex.org/C188521023","wikidata":"https://www.wikidata.org/wiki/Q6795644","display_name":"Maximal set","level":3,"score":0.5640806555747986},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.5613967776298523},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5337544083595276},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4972827732563019},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4875616431236267},{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.45759138464927673},{"id":"https://openalex.org/C179061269","wikidata":"https://www.wikidata.org/wiki/Q5263786","display_name":"Description number","level":5,"score":0.4418129324913025},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3112080991268158},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.280345618724823},{"id":"https://openalex.org/C131671149","wikidata":"https://www.wikidata.org/wiki/Q2703890","display_name":"Universal Turing machine","level":4,"score":0.083354651927948},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2274854","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274854","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/1183742911","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183742911","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W348975399","https://openalex.org/W1924816003","https://openalex.org/W1972481159","https://openalex.org/W1972685794","https://openalex.org/W2006726677","https://openalex.org/W2016891068","https://openalex.org/W2037416374","https://openalex.org/W2056414301","https://openalex.org/W2070390550","https://openalex.org/W2101746971","https://openalex.org/W2551720480","https://openalex.org/W4213156362","https://openalex.org/W4232277851"],"related_works":["https://openalex.org/W2484712192","https://openalex.org/W1604909338","https://openalex.org/W2739700767","https://openalex.org/W2490340048","https://openalex.org/W2183782096","https://openalex.org/W1924424002","https://openalex.org/W2186864846","https://openalex.org/W2083502326","https://openalex.org/W1982652937","https://openalex.org/W2393688265"],"abstract_inverted_index":{"Abstract":[0],"Work":[1],"in":[2,27,74,165],"the":[3,6,51,66,75,90,117,123,139],"setting":[4],"of":[5,68,77,109,141],"recursively":[7,61,132],"enumerable":[8,62],"sets":[9],"and":[10,29,44,48,103],"their":[11],"Turing":[12,23,118],"degrees.":[13],"A":[14,64,69,78,102,110,142,149,158,167],"set":[15,63,95,101],"X":[16,20,32],"is":[17,25,55,72,111,151,180,186,198],"low":[18,43,188,196],"if":[19,31,58],"\u2032,":[21],"its":[22,105],"jump,":[24],"recursive":[26,73,91],"\u2205\u2032":[28],"high":[30],"\u2032":[33],"computes":[34],"\u2205\u2033.":[35],"Attempting":[36],"to":[37,131,153],"find":[38],"a":[39,94,100,125,129,136,181,187],"property":[40],"between":[41],"being":[42,45],"recursive,":[46],"Bickford":[47],"Mills":[49],"produced":[50],"following":[52],"definition.":[53],"W":[54,71,96,134,147,173],"deep":[56,86,183],",":[57,65,97,143],"for":[59],"each":[60],"jump":[67,76],"\u2295":[70,148],".":[79,121,174],"We":[80,175],"prove":[81],"that":[82,145,178],"there":[83,179],"are":[84],"no":[85],"degrees":[87],"other":[88,195],"than":[89],"one.":[92],"Given":[93],"we":[98],"enumerate":[99],"approximate":[104],"jump.":[106],"The":[107,160],"construction":[108],"governed":[112],"by":[113,116],"strategies,":[114],"indexed":[115],"functionals":[119],"\u03a6":[120,156],"Simplifying":[122],"situation,":[124],"typical":[126],"strategy":[127],"converts":[128],"failure":[130],"compute":[133],"into":[135],"constraint":[137],"on":[138],"enumeration":[140],"so":[144],"(":[146],")\u2032":[150],"forced":[152],"disagree":[154],"with":[155,193],"(\u2212;":[157],"\u2032).":[159],"conversion":[161],"has":[162],"some":[163],"ambiguity;":[164],"particular,":[166],"cannot":[168],"be":[169],"found":[170],"uniformly":[171],"from":[172],"also":[176],"show":[177],"\u201cmoderately\u201d":[182],"degree:":[184],"There":[185],"nonzero":[189],"degree":[190,197],"whose":[191],"join":[192],"any":[194],"not":[199],"high.":[200]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
