{"id":"https://openalex.org/W2113069034","doi":"https://doi.org/10.2307/2271777","title":"On degrees of unsolvability and complexity properties","display_name":"On degrees of unsolvability and complexity properties","publication_year":1975,"publication_date":"1975-12-01","ids":{"openalex":"https://openalex.org/W2113069034","doi":"https://doi.org/10.2307/2271777","mag":"2113069034"},"language":"en","primary_location":{"id":"doi:10.2307/2271777","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271777","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/A5030528423","display_name":"Ivan Marques","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":true,"raw_author_name":"Ivan Marques","raw_affiliation_strings":["University Of California, Berkeley, California 94720","University of California , Berkeley, California, 94720"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University Of California, Berkeley, California 94720","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"University of California , Berkeley, California, 94720","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5030528423"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":1.5971,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.85920398,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"40","issue":"4","first_page":"529","last_page":"540"},"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":0.9948999881744385,"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":0.991599977016449,"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/recursively-enumerable-language","display_name":"Recursively enumerable language","score":0.9642525911331177},{"id":"https://openalex.org/keywords/recursively-enumerable-set","display_name":"Recursively enumerable set","score":0.8663736581802368},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6851032376289368},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.6757568717002869},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6613694429397583},{"id":"https://openalex.org/keywords/maximal-set","display_name":"Maximal set","score":0.6336743831634521},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.5641019940376282},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5597721338272095},{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.5572364330291748},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5544704794883728},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.549197256565094},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.46206530928611755},{"id":"https://openalex.org/keywords/computability-theory","display_name":"Computability theory","score":0.4468492269515991},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4389348030090332},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1886521875858307}],"concepts":[{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.9642525911331177},{"id":"https://openalex.org/C52703633","wikidata":"https://www.wikidata.org/wiki/Q676835","display_name":"Recursively enumerable set","level":3,"score":0.8663736581802368},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6851032376289368},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.6757568717002869},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6613694429397583},{"id":"https://openalex.org/C188521023","wikidata":"https://www.wikidata.org/wiki/Q6795644","display_name":"Maximal set","level":3,"score":0.6336743831634521},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.5641019940376282},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5597721338272095},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.5572364330291748},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5544704794883728},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.549197256565094},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.46206530928611755},{"id":"https://openalex.org/C111142201","wikidata":"https://www.wikidata.org/wiki/Q818930","display_name":"Computability theory","level":2,"score":0.4468492269515991},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4389348030090332},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1886521875858307},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2271777","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271777","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/1183739575","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183739575","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":5,"referenced_works":["https://openalex.org/W1975592766","https://openalex.org/W2057392475","https://openalex.org/W2070390550","https://openalex.org/W2089442854","https://openalex.org/W2905135108"],"related_works":["https://openalex.org/W2037833610","https://openalex.org/W2135152748","https://openalex.org/W2069987267","https://openalex.org/W1973052363","https://openalex.org/W1972481159","https://openalex.org/W1980641386","https://openalex.org/W2112189052","https://openalex.org/W4249600134","https://openalex.org/W798745779","https://openalex.org/W2186864846"],"abstract_inverted_index":{"In":[0,169],"this":[1,143],"paper":[2,144],"we":[3],"present":[4],"two":[5],"theorems":[6],"concerning":[7],"relationships":[8],"between":[9],"degrees":[10],"of":[11,13,60,71,90,108,120,137,155,164],"unsolvability":[12],"recursively":[14,29,34],"enumerable":[15,30,35],"sets":[16,31,47,74,125,140,158],"and":[17],"their":[18],"complexity":[19],"properties.":[20],"The":[21,94],"first":[22],"theorem":[23,39,96,113],"asserts":[24],"that":[25,43,55,98,123,174],"there":[26],"are":[27,48,127],"nonspeedable":[28,83],"in":[32,118],"every":[33,99],"Turing":[36,45,62],"degree.":[37],"This":[38,112],"disproves":[40],"the":[41,53,61,66,77,88,91,106,109,121,134,138,156,162,165],"conjecture":[42],"all":[44,124],"complete":[46,63],"speedable,":[49],"which":[50,126,159],"arose":[51],"from":[52],"fact":[54,122],"a":[56,82,151,178,180],"rather":[57],"inclusive":[58],"subclass":[59],"sets,":[64,68],"namely,":[65],"subcreative":[67],"consists":[69],"solely":[70],"effectively":[72],"speedable":[73,100,131,157],"[2].":[75],"Furthermore,":[76],"natural":[78],"construction":[79],"to":[80,86,129,133],"produce":[81],"set":[84,101,182],"seems":[85],"lower":[87],"degree":[89,177],"resulting":[92],"set.":[93],"second":[95],"says":[97],"has":[102],"jump":[103,107,132,136],"strictly":[104],"above":[105],"recursive":[110,139],"sets.":[111],"is":[114],"an":[115,175],"expected":[116],"one":[117],"view":[119],"known":[128],"be":[130],"double":[135],"[4].":[141],"After":[142],"was":[145],"written,":[146],"R.":[147],"Soare":[148],"[8]":[149],"found":[150],"very":[152],"useful":[153],"characterization":[154,172],"greatly":[160],"facilitated":[161],"proofs":[163],"results":[166],"presented":[167],"here.":[168],"addition":[170],"his":[171],"implies":[173],"r.e.":[176],"contains":[179],"speed-able":[181],"iff":[183],"a\u2032":[184],">":[185],"0\u2032.":[186]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}