{"id":"https://openalex.org/W2029458268","doi":"https://doi.org/10.1305/ndjfl/1093870220","title":"A note on intuitionistic models of ${\\rm ZF}$.","display_name":"A note on intuitionistic models of ${\\rm ZF}$.","publication_year":1983,"publication_date":"1983-01-01","ids":{"openalex":"https://openalex.org/W2029458268","doi":"https://doi.org/10.1305/ndjfl/1093870220","mag":"2029458268"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093870220","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093870220","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/A5111816006","display_name":"R. Lavendhomme","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"R. Lavendhomme","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5070742118","display_name":"Tom Lucas","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"T. Lucas","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111816006"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.13116465,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"24","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9807000160217285,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9807000160217285,"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/T10456","display_name":"Multi-Agent Systems and Negotiation","score":0.9286999702453613,"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/T10991","display_name":"Game Theory and Voting Systems","score":0.9222000241279602,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.6973499059677124},{"id":"https://openalex.org/keywords/sketch","display_name":"Sketch","score":0.6719170212745667},{"id":"https://openalex.org/keywords/sheaf","display_name":"Sheaf","score":0.6116565465927124},{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.5728380680084229},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5390531420707703},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4380197525024414},{"id":"https://openalex.org/keywords/kripke-semantics","display_name":"Kripke semantics","score":0.4375571012496948},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.42655694484710693},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.4036584496498108},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.4000414311885834},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37418776750564575},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36039891839027405},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29970091581344604},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.20344746112823486},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.20046916604042053},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17691466212272644},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.17160239815711975},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.14652305841445923},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.12096691131591797},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.057626575231552124}],"concepts":[{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.6973499059677124},{"id":"https://openalex.org/C2779231336","wikidata":"https://www.wikidata.org/wiki/Q7534724","display_name":"Sketch","level":2,"score":0.6719170212745667},{"id":"https://openalex.org/C4017995","wikidata":"https://www.wikidata.org/wiki/Q595298","display_name":"Sheaf","level":2,"score":0.6116565465927124},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.5728380680084229},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5390531420707703},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4380197525024414},{"id":"https://openalex.org/C160131679","wikidata":"https://www.wikidata.org/wiki/Q2462350","display_name":"Kripke semantics","level":4,"score":0.4375571012496948},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.42655694484710693},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.4036584496498108},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.4000414311885834},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37418776750564575},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36039891839027405},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29970091581344604},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.20344746112823486},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.20046916604042053},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17691466212272644},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.17160239815711975},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.14652305841445923},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.12096691131591797},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.057626575231552124},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1093870220","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093870220","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/1093870220","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093870220","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":[{"display_name":"Reduced inequalities","score":0.4699999988079071,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W355150914","https://openalex.org/W1996099995","https://openalex.org/W2064461340"],"related_works":["https://openalex.org/W2403418519","https://openalex.org/W2074934605","https://openalex.org/W4205932853","https://openalex.org/W2482057698","https://openalex.org/W2163197731","https://openalex.org/W2952481855","https://openalex.org/W2055558461","https://openalex.org/W2002701178","https://openalex.org/W3145584637","https://openalex.org/W2754467536"],"abstract_inverted_index":{"An":[0],"analysis":[1],"of":[2,6,8,12,49,54,57,122,125,159,161,184,187,200,230,233,239,266,271,283,293],"the":[3,47,111,114,123,137,157,177,181,197,213,215,225,245,257,263,272,294,305],"forcing":[4,82,92],"construction":[5,158,178,183,292],"models":[7,160,186],"ZF":[9,162,188],"by":[10,24,237],"means":[11],"intuitionistic":[13,63,281,291],"logic":[14],"and":[15,104,173,256,275,304],"Kripke":[16],"semantics":[17],"(or":[18],"sheaf":[19,56,97,147],"semantics)":[20],"has":[21],"been":[22],"made":[23],"many":[25],"authors":[26],"(see":[27],"for":[28,134,287],"example":[29,288],"[":[30],"1":[31],"],":[32],"[2],":[33,242],"[5]).We":[34],"feel":[35],"however":[36],"that":[37,89],"some":[38],"basic":[39],"information":[40],"is":[41,116,129,150,163,222,249,270,289,300],"still":[42],"available":[43],"from":[44,110,224],"this":[45,65,169,298],"approach,":[46],"motto":[48],"which":[50,85,175],"could":[51],"be":[52,217,277],"\"think":[53],"a":[55,60,80,120,126,191,231,235],"structures":[58,148],"as":[59,142,149,190,279],"structure,":[61],"using":[62],"logic\".In":[64],"note,":[66],"we":[67,170,205],"are":[68,95,139],"not":[69,301],"really":[70],"interested":[71],"in":[72,131,152,165,262],"obtaining":[73],"independence":[74],"results,":[75],"but":[76,136],"want":[77],"to":[78,113,143,146,156,180,195,211,253],"sketch":[79],"set-theoretic":[81],"along":[83],"lines":[84],"closely":[86],"agree":[87],"with":[88],"motto.In":[90],"usual":[91],"constructions,":[93],"there":[94],"two":[96,209],"structures:":[98],"<M,":[99],"-e":[100],"p":[101],"-)":[102],"peC":[103,107],"(M,p":[105],"lh-e->":[106],",and":[108],"passing":[109],"first":[112,295],"second":[115,273],"nothing":[117],"else":[118],"than":[119],"sheaf-version":[121],"extensionalization":[124],"binary":[127],"relation.This":[128],"discussed":[130],"Section":[132,153,166],"2":[133],"Kripke-structures":[135],"proofs":[138],"designed":[140],"so":[141,302],"immediately":[144],"extend":[145],"indicated":[151],"4.":[154],"Application":[155],"given":[164],"3.":[167],"To":[168],"add":[171],"definitions":[172],"notions":[174],"bring":[176],"closer":[179],"classical":[182],"inner":[185],"and,":[189],"\"test-case\",":[192],"indicate":[193],"how":[194],"adapt":[196],"well-known":[198],"proof":[199],"relative":[201],"consistency":[202],"o\u03caV\u03a6L.Roughly":[203],"speaking,":[204],"may":[206,276],"distinguish":[207],"between":[208],"approaches":[210],"forcing.In":[212],"first,":[214],"model,":[216],"it":[218],"Boolean-valued":[219],"or":[220],"intuitionistic,":[221],"constructed":[223],"base":[226],"model":[227],"Masa":[228],"union":[229],"sequence":[232],"M":[234,240],"indexed":[236],"ordinals":[238],"([1],":[241],"[4],":[243],"[5]).In":[244],"second,":[246],"no":[247],"hierarchy":[248,258],"present,":[250],"at":[251],"least":[252],"begin":[254],"with,":[255],"effect":[259],"remains":[260],"concentrated":[261],"various":[264],"forms":[265],"induction":[267],"[7].Our":[268],"approach":[269],"kind":[274],"viewed":[278],"an":[280,290],"version":[282],"[7],":[284],"whereas":[285],"[2]":[286],"kind.In":[296],"fact,":[297],"distinction":[299],"clear-cut":[303]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
