{"id":"https://openalex.org/W2047187027","doi":"https://doi.org/10.2307/2272826","title":"Diagonalization in degree constructions","display_name":"Diagonalization in degree constructions","publication_year":1978,"publication_date":"1978-06-01","ids":{"openalex":"https://openalex.org/W2047187027","doi":"https://doi.org/10.2307/2272826","mag":"2047187027"},"language":"en","primary_location":{"id":"doi:10.2307/2272826","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2272826","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/A5061564964","display_name":"Daniel Posner","orcid":"https://orcid.org/0000-0003-3868-3401"},"institutions":[{"id":"https://openalex.org/I2803209242","display_name":"University of California System","ror":"https://ror.org/00pjdza24","country_code":"US","type":"education","lineage":["https://openalex.org/I2803209242"]},{"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":"D. Posner","raw_affiliation_strings":["University of California, Berkeley, California 94720","University of California"],"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","institution_ids":["https://openalex.org/I2803209242"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063367613","display_name":"Richard L. Epstein","orcid":null},"institutions":[{"id":"https://openalex.org/I41156924","display_name":"Victoria University of Wellington","ror":"https://ror.org/0040r6f76","country_code":"NZ","type":"education","lineage":["https://openalex.org/I41156924"]},{"id":"https://openalex.org/I4210137805","display_name":"Victoria School of Management","ror":"https://ror.org/03yvdgx21","country_code":"CH","type":"education","lineage":["https://openalex.org/I4210137805"]}],"countries":["CH","NZ"],"is_corresponding":false,"raw_author_name":"R. Epstein","raw_affiliation_strings":["Victoria University, Wellington, New Zealand","Victoria University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Victoria University, Wellington, New Zealand","institution_ids":["https://openalex.org/I41156924"]},{"raw_affiliation_string":"Victoria University","institution_ids":["https://openalex.org/I4210137805"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.5243,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.63922156,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"43","issue":"2","first_page":"280","last_page":"283"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9973000288009644,"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":0.9973000288009644,"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":0.9763000011444092,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9452000260353088,"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/combinatorics","display_name":"Combinatorics","score":0.7002820372581482},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.6441866159439087},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5479497909545898},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5460129976272583},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5442342162132263},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5309932231903076},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.530261218547821},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.45225149393081665},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4490450620651245},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40002426505088806},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24667972326278687},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.06907457113265991}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7002820372581482},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.6441866159439087},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5479497909545898},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5460129976272583},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5442342162132263},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5309932231903076},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.530261218547821},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.45225149393081665},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4490450620651245},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40002426505088806},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24667972326278687},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.06907457113265991},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2272826","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2272826","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/1183740204","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183740204","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":5,"referenced_works":["https://openalex.org/W2079464688","https://openalex.org/W2145265838","https://openalex.org/W2160667926","https://openalex.org/W2319599413","https://openalex.org/W3159824982"],"related_works":["https://openalex.org/W2032233321","https://openalex.org/W3121970507","https://openalex.org/W2110028391","https://openalex.org/W54497855","https://openalex.org/W217960748","https://openalex.org/W3161230432","https://openalex.org/W3125814499","https://openalex.org/W2090827041","https://openalex.org/W2565703248","https://openalex.org/W187246281"],"abstract_inverted_index":{"We":[0,29,37,139,161],"present":[1],"two":[2],"theorems":[3],"whose":[4],"applications":[5],"are":[6,215],"to":[7,70,102,169,181],"eliminate":[8],"diagonalization":[9],"arguments":[10],"from":[11,25,179],"a":[12,31,39,67,71,154,184],"variety":[13],"of":[14,16,18,34,66,75,81,100,121,156,198],"constructions":[15],"degrees":[17],"unsolvability.":[19],"All":[20],"definitions":[21],"and":[22,51,133,148,191,218],"notations":[23],"come":[24],"[1,":[26],"Chapter":[27],"1].":[28],"give":[30],"brief":[32],"resum\u00e9":[33],"them":[35],"here.":[36],"identify":[38],"set":[40,93],"with":[41],"its":[42],"characteristic":[43,68],"function.":[44],"(A(x)=":[45],"1":[46,86,125],"if":[47,56,87,144,171,186,196],"x":[48,57],"\u2208":[49],"A":[50,52,60,101,175],"(x)":[53],"=":[54,79,83,89,109,137,173],"0":[55,110],"\u2209":[58],"A.)":[59],"string":[61,120],"\u03c3":[62,82,88,113,128,132,134,141,145],"is":[63,97,116,153,166,183,188,205],"the":[64,98,119,157],"restriction":[65,99],"function":[69],"finite":[72],"initial":[73],"segment":[74],"natural":[76],"numbers,":[77],"lh(\u03c3)":[78,123],"length":[80,122],"n":[84],"+":[85,124],"A[n]":[90],"for":[91,192],"some":[92],"A.":[94],"(A":[95],"[n]":[96],"{m:":[103],"m":[104],"\u2264":[105],"n}.)":[106],"If":[107],"i":[108,115,130],"or":[111],"1,":[112],"*":[114,129,135,200,203,210,213,220,222],"defined":[117,206,217],"as":[118],"such":[126],"that":[127],"\u2287":[131],"i(lh(\u03c3))":[136],"i.":[138],"write":[140,162],"\u2223":[142],"\u03c4":[143,147,149],"\u2289":[146,150],"\u03c3.":[151],"{\u03a6n}":[152],"listing":[155],"partial":[158,176],"recursive":[159],"functionals.":[160],"\u201cA":[163],"\u2264TB\u201d":[164],"(\u201cA":[165],"Turing":[167],"reducible":[168],"B\u201d)":[170],"\u2203n\u2200x\u03a6n(B)(x)":[172],"A(x).":[174],"function,":[177],"T,":[178],"strings":[180,182],"tree":[185],"T":[187],"order":[189],"preserving":[190],"all":[193,216],"strings,":[194],"\u03c3,":[195],"one":[197],"T(\u03c3":[199,202,209,212,219],"0),":[201,211],"1)":[204,214],"then":[207],"T(\u03c3),":[208],"0)\u2223(\u03c3":[221],"1).":[223]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}