{"id":"https://openalex.org/W2124831295","doi":"https://doi.org/10.2307/2267047","title":"Note on an idea of Fitch","display_name":"Note on an idea of Fitch","publication_year":1949,"publication_date":"1949-09-01","ids":{"openalex":"https://openalex.org/W2124831295","doi":"https://doi.org/10.2307/2267047","mag":"2124831295"},"language":"en","primary_location":{"id":"doi:10.2307/2267047","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2267047","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/A5060119550","display_name":"John Myhill","orcid":null},"institutions":[{"id":"https://openalex.org/I126820664","display_name":"Vassar College","ror":"https://ror.org/022x6qg61","country_code":"US","type":"education","lineage":["https://openalex.org/I126820664"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"John R. Myhill","raw_affiliation_strings":["Vassar College"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Vassar College","institution_ids":["https://openalex.org/I126820664"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060119550"],"corresponding_institution_ids":["https://openalex.org/I126820664"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.1838843,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"3","first_page":"175","last_page":"176"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9861000180244446,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9861000180244446,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.980400025844574,"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":0.9772999882698059,"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":0.6648876070976257},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5653207302093506},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.5645901560783386},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4340086579322815},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.43214693665504456},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.382895827293396},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3774033188819885},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25665056705474854},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0999043881893158}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6648876070976257},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5653207302093506},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.5645901560783386},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4340086579322815},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.43214693665504456},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.382895827293396},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3774033188819885},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25665056705474854},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0999043881893158},{"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2267047","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2267047","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/1183730669","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183730669","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":1,"referenced_works":["https://openalex.org/W4256369010"],"related_works":["https://openalex.org/W2399035783","https://openalex.org/W3161230432","https://openalex.org/W1487201914","https://openalex.org/W4367190712","https://openalex.org/W280458463","https://openalex.org/W1170131723","https://openalex.org/W4301429470","https://openalex.org/W4246276930","https://openalex.org/W2074733683","https://openalex.org/W2007089758"],"abstract_inverted_index":{"The":[0],"concept":[1],"of":[2,7,20,60,71,81,90,123,183,189,194],"a":[3,72,120],"recursively":[4,29,36,52,65],"definite":[5,37,53],"predicate":[6,27,175],"natural":[8],"numbers":[9],"was":[10],"introduced":[11],"by":[12],"F.":[13],"B.":[14],"Fitch":[15],"in":[16,181],"his":[17],"An":[18,173],"extension":[19],"basic":[21],"logic":[22],"as":[23,76],"follows:":[24,77],"Every":[25],"recursive":[26],"is":[28,35,39,51,56,64,74,80,92,112,119,161,169,176,179],"definite.":[30],"If":[31,49],"R(x1,":[32],"\u2026,":[33,41,46,101,104,107,110,126,129,131,133,138,141,144,147,149,152,159,163,167,171],"xn)":[34],"so":[38],"(Ey)R(x1,":[40],"xn\u22121,":[42,47],"y)":[43],"and":[44,54,115,165,187,199],"(y)R(x1,":[45],"y).":[48],"R":[50,79,91],"S":[55,63,95],"the":[57,68,87,93,184,192,195],"proper":[58,69,88],"ancestral":[59,70,89],"R,":[61],"then":[62,86],"definite,":[66],"where":[67,157],"relation":[73,94],"defined":[75],"if":[78,114,117],"even":[82],"degree,":[83],"say":[84],"2m,":[85],"such":[96,135],"that":[97,136],"for":[98],"all":[99,155],"x1,":[100],"xm,":[102,108],"y1,":[103,109],"ym,":[105],"S(x1,":[106],"ym)":[111],"true":[113],"only":[116],"there":[118],"finite":[121],"sequence":[122],"sequences":[124],"(z11,":[125,158],"zm1),":[127],"(z12,":[128],"Zm2),":[130],"(z1k,":[132,166],"Zmk)":[134,153],"R(Z11,":[137],"Zm1,":[139],"z12,":[140],"zm2),":[142],"R(z12,":[143],"zm2,":[145],"z13,":[146],"zm3),":[148],"R(z1,k\u22121,":[150],"z1k,":[151],"are":[154],"true,":[156],"zm1)":[160],"(x1,":[162],"xm)":[164],"zmk)":[168],"(y1,":[170],"ym).":[172],"arithmetic":[174],"one":[177],"which":[178],"definable":[180],"terms":[182],"operations":[185],"\u2018+\u2019":[186],"\u2018\u00b7\u2019":[188],"elementary":[190],"arithmetic,":[191],"connectives":[193],"classical":[196],"prepositional":[197],"calculus,":[198],"quantifiers.":[200]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}