{"id":"https://openalex.org/W1982691200","doi":"https://doi.org/10.1305/ndjfl/1093893706","title":"Selection functions for recursive functionals.","display_name":"Selection functions for recursive functionals.","publication_year":1969,"publication_date":"1969-07-01","ids":{"openalex":"https://openalex.org/W1982691200","doi":"https://doi.org/10.1305/ndjfl/1093893706","mag":"1982691200"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093893706","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093893706","pdf_url":null,"source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal 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/A5086335726","display_name":"Thomas J. Grilliot","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Thomas J. Grilliot","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5086335726"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.7931,"has_fulltext":true,"cited_by_count":32,"citation_normalized_percentile":{"value":0.93995997,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"10","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9564999938011169,"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"}},"topics":[{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9564999938011169,"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"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9059000015258789,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.7223654389381409},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49419406056404114},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4046016335487366},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3760960102081299},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.35085999965667725},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.35020411014556885},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22378328442573547},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.05569830536842346}],"concepts":[{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.7223654389381409},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49419406056404114},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4046016335487366},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3760960102081299},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.35085999965667725},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.35020411014556885},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22378328442573547},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.05569830536842346},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1093893706","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093893706","pdf_url":null,"source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1093893706","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093893706","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":6,"referenced_works":["https://openalex.org/W1526907582","https://openalex.org/W2033831013","https://openalex.org/W2100003518","https://openalex.org/W2339460772","https://openalex.org/W4250432112","https://openalex.org/W6675014228"],"related_works":["https://openalex.org/W2606073172","https://openalex.org/W2125356288","https://openalex.org/W2128302072","https://openalex.org/W2970622411","https://openalex.org/W4230623537","https://openalex.org/W2063488590","https://openalex.org/W4239376463","https://openalex.org/W2351859806","https://openalex.org/W1994109492","https://openalex.org/W1987371472"],"abstract_inverted_index":{"Many":[0],"of":[1,8,11,33,60,68,76,91,93,137,155,159,239,246,289,307],"the":[2,6,19,31,37,58,65,102,128,131,135,153,187,214,226,236,244,256,287,300,305,308],"interesting":[3],"results":[4,56,161],"in":[5,40,57,127,140,170,196,232],"study":[7],"recursive":[9,23,241],"functions":[10,24,67,84,107,139,242,262],"finite":[12],"higher":[13,43,270],"types":[14,288],"owe":[15],"their":[16],"existence":[17,136],"to":[18,53,117,163,254,260,275,285],"way":[20],"that":[21,85,100,108,124,167,193,235,299],"partial":[22,240],"can":[25,199],"be":[26,200],"defined":[27,62,120,157],"inductively":[28,61,119,156],"by":[29,96,181,202,208,220],"schemes.However,":[30],"profusion":[32],"notation":[34,306],"sometimes":[35],"clouds":[36],"techniques":[38],"involved":[39],"working":[41],"with":[42,304],"types.For":[44],"greater":[45],"clarity":[46],"and":[47,79,143,148,192,219,266],"possible":[48],"generalization":[49,274,282],"it":[50],"is":[51,302],"natural":[52],"reinvestigate":[54],"these":[55],"setting":[59,154],"sets.In":[63],"particular,":[64],"selection":[66,164,261],"Gandy":[69,209],"[l,":[70,210],"p.":[71,77,211],"14],":[72],"Moschovakis":[73,182,221],"[3,":[74,183,222],"(I)":[75],"270]":[78],"Platek":[80],"[4,":[81],"are":[82,101,106,125,150,175,252,294],"basically":[83],"choose":[86,109],"from":[87,110,277],"a":[88,203,273],"countable":[89],"set":[90,121,129],"trees":[92,99],"computation":[94],"(indexed":[95],"numbers)":[97],"those":[98,122],"shortest.More":[103],"abstractly,":[104],"they":[105],"some":[111],"objects":[112,123],"(some":[113],"of)":[114],"which":[115,292],"belong":[116],"an":[118],"placed":[126],"at":[130],"earliest":[132],"stage.We":[133],"prove":[134],"such":[138],"Theorems":[141,146,247],"1":[142,248],"2.":[144],"Our":[145],"3":[147],"4":[149],"analogues":[151],"(in":[152],"sets)":[158],"two":[160],"related":[162,259],"functions;":[165],"namely,":[166],"sets":[168,279],"r.e.":[169,195],"E":[171,197],"n+2":[172,198],"(n":[173],">0)":[174],"not":[176],"closed":[177,295],"under":[178,291],"type-?zquantification":[179],"(proved":[180,207],"Theorem":[184,223,233],"10]":[185],"for":[186,213,225,268],"case":[188,215,227],"n":[189,216,228],"=":[190,217,229],"1),":[191],"predicates":[194],"characterized":[201],"bounded":[204],"existential-quantifier":[205],"form":[206],"17]":[212],"0":[218],"9]":[224],"1).By":[230],"showing":[231],"5":[234],"inductive":[237],"definition":[238],"fits":[243],"hypotheses":[245],"through":[249],"4,":[250],"we":[251],"able":[253],"obtain":[255],"known":[257],"theorems":[258],"(Theorems":[263],"6,":[264],"7":[265],"8)":[267],"all":[269],"types,":[271],"plus":[272],"selections":[276],"uncountable":[278],"(Theorem":[280,296],"6).This":[281],"enables":[283],"us":[284],"characterize":[286],"quantification":[290],"r.e.predicates":[293],"9).We":[297],"assume":[298],"reader":[301],"familiar":[303],"first":[309],"half":[310]},"counts_by_year":[{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2025-10-10T00:00:00"}
