{"id":"https://openalex.org/W2041037160","doi":"https://doi.org/10.1305/ndjfl/1093882938","title":"Reflections on an extensionality theorem.","display_name":"Reflections on an extensionality theorem.","publication_year":1980,"publication_date":"1980-01-01","ids":{"openalex":"https://openalex.org/W2041037160","doi":"https://doi.org/10.1305/ndjfl/1093882938","mag":"2041037160"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093882938","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093882938","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-21/issue-1/Reflections-on-an-extensionality-theorem/10.1305/ndjfl/1093882938.pdf","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":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-21/issue-1/Reflections-on-an-extensionality-theorem/10.1305/ndjfl/1093882938.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050356327","display_name":"Philip Hugly","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Philip Hugly","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5050356327"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18271768,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"21","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.4253999888896942,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.4253999888896942,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.3874000012874603,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/extensionality","display_name":"Extensionality","score":0.9635884761810303},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49043509364128113},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4680129289627075},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3441011309623718},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2987414598464966},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.162214994430542},{"id":"https://openalex.org/keywords/orthodontics","display_name":"Orthodontics","score":0.04427415132522583}],"concepts":[{"id":"https://openalex.org/C150355047","wikidata":"https://www.wikidata.org/wiki/Q965432","display_name":"Extensionality","level":2,"score":0.9635884761810303},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49043509364128113},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4680129289627075},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3441011309623718},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2987414598464966},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.162214994430542},{"id":"https://openalex.org/C29694066","wikidata":"https://www.wikidata.org/wiki/Q118301","display_name":"Orthodontics","level":1,"score":0.04427415132522583}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1093882938","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093882938","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-21/issue-1/Reflections-on-an-extensionality-theorem/10.1305/ndjfl/1093882938.pdf","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/1093882938","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093882938","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":{"id":"doi:10.1305/ndjfl/1093882938","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093882938","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-21/issue-1/Reflections-on-an-extensionality-theorem/10.1305/ndjfl/1093882938.pdf","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2041037160.pdf","grobid_xml":"https://content.openalex.org/works/W2041037160.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2922343235","https://openalex.org/W4387963895","https://openalex.org/W2572376253","https://openalex.org/W2064861136","https://openalex.org/W2762953140","https://openalex.org/W1895537820","https://openalex.org/W2149318139","https://openalex.org/W358049013","https://openalex.org/W3106670512","https://openalex.org/W3138716284"],"abstract_inverted_index":{"HUGLY":[0],"1":[1],"Like":[2],"any":[3],"artifact,":[4],"a":[5,37,53,66,73,83,105,122,318],"formal":[6,38],"language":[7,39,46,62,92,97,130,321],"may":[8,296],"not":[9,88,149,172,251,262],"coincide":[10],"with":[11,14,158,282],"the":[12,45,61,70,76,79,91,96,125,129,155,199,210,240,243,259,264],"intention":[13],"which":[15,159,274],"it":[16,30,56,170],"was":[17,31,63,276],"constructed,":[18],"either":[19],"by":[20,27],"having":[21],"unanticipated":[22],"but":[23],"important":[24],"properties":[25,29],"or":[26,42,179],"lacking":[28,82],"intended":[32,49,99,113],"to":[33,57,64,100,114,150,217,237,258,263,290],"have.Some":[34],"theorems":[35],"about":[36],"assert,":[40],"directly":[41],"indirectly,":[43],"that":[44,60,81,107,223,292],"has":[47,220],"certain":[48,67],"properties.Formulation":[50],"of":[51,69,75,132,181,198,209,242,248,267,273,294,300],"such":[52],"theorem":[54,77,116,200,244],"brings":[55],"explicit":[58],"awareness":[59],"have":[65,109,214],"property.Recognition":[68],"need":[71,180,247],"for":[72,128,142],"proof":[74,84,102,127,182,197,212,225],"is":[78,95,104,201,207,230,236,304,317],"recognition":[80],"one":[85,98],"simply":[86],"does":[87,171],"know":[89,252],"whether":[90,253],"actually":[93],"constructed":[94,110],"construct.The":[101,115],"itself":[103],"check":[106],"we":[108,112],"what":[111],"this":[117,168,303],"paper":[118,191],"investigates":[119],"functions":[120],"as":[121],"lemma":[123],"in":[124,188,286,311],"soundness":[126],"\u00a3":[131],"Mates'":[133],"rigorous":[134],"and":[135,204,229,245,261,279,326,329],"concise":[136],"text":[137],"Elementary":[138],"Logic":[139],"[l].Its":[140],"versions":[141],"other":[143,283],"systems":[144],"will":[145,307],"be":[146,298,308],"obvious":[147],"enough":[148],"require":[151],"separate":[152],"comment.2":[153],"Of":[154],"logic":[156,287],"texts":[157],"I":[160,213,275],"am":[161],"familiar":[162],"only":[163,211,257],"Mates":[164,219],"[l]":[165],"explicitly":[166],"notes":[167],"theorem.But":[169],"comment":[173],"on":[174,239],"its":[175,186,246],"general":[176],"content,":[177],"significance,":[178],"even":[183],"apart":[184],"from":[185],"role":[187],"proving":[189],"soundness.This":[190],"aims":[192],"at":[193],"filling":[194],"those":[195,227],"gaps.The":[196],"both":[202],"lengthy":[203],"complex":[205],"(that":[206],"true":[208],"been":[215],"able":[216],"devise;":[218],"told":[221],"me":[222,289],"his":[224],"shares":[226],"properties)":[228],"omitted":[231],"here.My":[232],"sole":[233],"present":[234],"concern":[235],"reflect":[238],"significance":[241],"proof.I":[249],"do":[250],"these":[254,301,313],"reflections":[255],"belong":[256],"technical":[260],"philosophical":[265],"side":[266],"logic.My":[268],"main":[269],"points":[270,314],"are":[271],"ones":[272],"long":[277],"unaware":[278],"my":[280],"conversations":[281],"philosophers":[284],"interested":[285],"lead":[288],"guess":[291],"many":[293],"them":[295],"also":[297],"unware":[299],"points.K":[302],"so,":[305],"there":[306],"some":[309],"value":[310],"making":[312],"obvious.3":[315],"X":[316],"standard":[319],"first-order":[320],"including":[322],"predicates,":[323],"individual":[324],"constants":[325],"variables,":[327],"connectives,":[328],"quantifiers.'Formula',":[330],"'free":[331]},"counts_by_year":[],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}