{"id":"https://openalex.org/W2798583139","doi":"https://doi.org/10.2307/2268281","title":"The \u00fe-function in \u03bb-<i>K</i>-conversion","display_name":"The \u00fe-function in \u03bb-<i>K</i>-conversion","publication_year":1937,"publication_date":"1937-12-01","ids":{"openalex":"https://openalex.org/W2798583139","doi":"https://doi.org/10.2307/2268281","mag":"2798583139"},"language":"en","primary_location":{"id":"doi:10.2307/2268281","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2268281","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/A5066565862","display_name":"Alan Turing","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A. M. Turing","raw_affiliation_strings":["Princeton University"],"affiliations":[{"raw_affiliation_string":"Princeton University","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066565862"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.09174664,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2","issue":"4","first_page":"164","last_page":"164"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9265999794006348,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9265999794006348,"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":0.6815396547317505},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6726347804069519},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5484673380851746},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5397335886955261},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.5105896592140198},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4308410882949829},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3494473099708557},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08058610558509827}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6815396547317505},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6726347804069519},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5484673380851746},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5397335886955261},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.5105896592140198},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4308410882949829},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3494473099708557},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08058610558509827},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2268281","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2268281","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W1964062928","https://openalex.org/W2325612495"],"related_works":["https://openalex.org/W1861401731","https://openalex.org/W1651031009","https://openalex.org/W1988718473","https://openalex.org/W2052299349","https://openalex.org/W1901944325","https://openalex.org/W2582753012","https://openalex.org/W3092439233","https://openalex.org/W4298858065","https://openalex.org/W205467172","https://openalex.org/W2007089758"],"abstract_inverted_index":{"In":[0],"the":[1,21,46,103,107,136,173,273,276],"theory":[2],"of":[3,35],"conversion":[4],"it":[5],"is":[6,39,80,100,270],"important":[7],"to":[8,16,44,82,102,259,272],"have":[9,172],"a":[10,30,37,64,72,83,86,92,132,262],"formally":[11],"defined":[12],"function":[13],"which":[14,28,53,75,119,283],"assigns":[15],"any":[17],"positive":[18,279],"integer":[19,23,280],"n":[20,27,78,90,268,277],"least":[22,108],"not":[24,113],"less":[25,114],"than":[26,115],"has":[29],"given":[31],"property.":[32],"The":[33,127,168],"definition":[34],"such":[36,67,264],"formula":[38,48,65,73,84,104,133,163,169,274],"somewhat":[40],"involved:":[41],"I":[42,59],"propose":[43],"give":[45],"corresponding":[47],"in":[49,61],"\u03bb-":[50],"K":[51],"-conversion,":[52],"will":[54,171,205],"(naturally)":[55],"be":[56,71,206],"much":[57],"simpler.":[58],"shall":[60],"fact":[62],"find":[63],"\u00fe":[66,170,231],"that":[68,138,265],"if":[69,150,176,208,230],"T":[70,76,120,184,214,221,284],"for":[74,118,282],"(":[77,121,159,185,199,215,224,237,244,248,266,285],")":[79,99,123,154,180,187,194,212,269,287],"convertible":[81,101,271],"representing":[85,106,275],"natural":[87,93,109],"number,":[88,94],"whenever":[89],"represents":[91],"then":[95,155],"\u00fe(":[96,177,191,196,209],"T,":[97,178,192,197,210,267],"r":[98,116,179,182,186,193,200,211,216,225,227,238,249,251],"q":[105,111,122,281,286],"number":[110],",":[112,117,217,222,239,246],"conv":[124,140,157,181,188,195,213,232,288],"0.":[125,289],"2":[126],"method":[128],"depends":[129],"on":[130],"finding":[131],"\u0398":[134,139],"with":[135,164],"property":[137,166,175],"\u03bb":[141,218,240],"u":[142,144,146],"\u00b7":[143,235,242],"(\u0398(":[145],")),":[147,226,250],"and":[148,190],"consequently":[149],"M":[151,156,160],"\u2192\u0398(":[152],"V":[153,158],").":[161],"A":[162],"this":[165],"is,":[167],"required":[174],"when":[183],"0,":[189],"S":[198,223,247],"))":[201],"otherwise.":[202],"These":[203],"conditions":[204],"satisfied":[207],"x":[219,241],"\u00b7\u00fe(":[220],"),":[228],"i.e.":[229],"{\u03bb":[233],"ptr":[234],"t":[236,245],"p":[243],")}(\u00fe).":[252],"We":[253],"therefore":[254],"put,":[255],"This":[256],"enables":[257],"us":[258],"define":[260],"also":[261],"formula,":[263],"th":[278]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
