{"id":"https://openalex.org/W2042191249","doi":"https://doi.org/10.1305/ndjfl/1093956429","title":"Independence of Tarski's law in Henkin's propositional fragments.","display_name":"Independence of Tarski's law in Henkin's propositional fragments.","publication_year":1960,"publication_date":"1960-01-01","ids":{"openalex":"https://openalex.org/W2042191249","doi":"https://doi.org/10.1305/ndjfl/1093956429","mag":"2042191249"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093956429","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093956429","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/A5109366683","display_name":"Ivo Thomas","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ivo Thomas","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5109366683"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.18622256,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"1","issue":"1-2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.8932999968528748,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.8932999968528748,"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/T10215","display_name":"Semantic Web and Ontologies","score":0.8245000243186951,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.8170999884605408,"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/propositional-calculus","display_name":"Propositional calculus","score":0.524905800819397},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.49365290999412537},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4884880781173706},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.46066656708717346},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3960937261581421},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.33447161316871643},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33425235748291016},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07678097486495972},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.05665993690490723}],"concepts":[{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.524905800819397},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.49365290999412537},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4884880781173706},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.46066656708717346},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3960937261581421},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.33447161316871643},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33425235748291016},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07678097486495972},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.05665993690490723},{"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/1093956429","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093956429","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/1093956429","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093956429","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":[{"score":0.5199999809265137,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W2083616448"],"related_works":["https://openalex.org/W3125750421","https://openalex.org/W2949765904","https://openalex.org/W4306949324","https://openalex.org/W4388544318","https://openalex.org/W618363683","https://openalex.org/W1978104062","https://openalex.org/W636031027","https://openalex.org/W1518756697","https://openalex.org/W2073983920","https://openalex.org/W2485140362"],"abstract_inverted_index":{"The":[0,39],"system":[1,6,43,162,299],"{A1-3,":[2],"(<P)*}":[3],"is":[4,34,44,74,92,111,131,198,237,241,257,273,295,304],"the":[5,42,47,86,97,167,194,204,217,234,242,298],"of":[7,41,61,104,142,196,219,225,246,263,283],"Henkin's":[8],"Q],":[9],"proved":[10],"by":[11],"him":[12],"complete":[13],"for":[14,210,228,313],"tautologies":[15],"in":[16,71,85,96,140,160,189,200,233,275,278,288,292,297],"implication":[17],"and":[18,54,109,183,207,268,280],"whatever":[19],"truth-function":[20],"<P":[21],"(x":[22],"..":[23],".,":[24,127],"x":[25,77,128],"m":[26,30,63,107,113,129],")":[27,130],"may":[28],"be.If":[29],"=":[31],"0,":[32],"\u03c8":[33,256,264],"just":[35],"T":[36,93,132,277,287,291],"or":[37,76,94,115,133],"F.":[38,134],"basis":[40],"modus":[45],"ponenSy":[46],"axiom":[48,64],"schemata":[49,65],"Al.Aj.BjA":[50],"A2.AjB^.A-2(B^C)^.AjC":[51],"A3.A-jC":[52],"J.AjBjCjC":[53],"a":[55,82,153,170,226,267,293],"set,":[56],"(":[57],"\u03c6":[58,272],")\u2022":[59],",":[60,124,255,265],"2":[62],"x*":[66,73],"j.x*":[67],"D":[68],".O":[69],"*S,D*>'":[70],"which":[72],"x.":[75],".3":[78],"y":[79,81],"(with":[80],"new":[83],"variable)":[84],"/-th":[87],"schema":[88],"according":[89,119],"as":[90,120],"%\u03b9":[91],"F":[95,274],"-th":[98],"valuation":[99],"(according":[100],"to":[101,212,310],"some":[102],"ordering)":[103],"<?(*,,...,":[105],"*":[106],"),":[108,216],"<P*":[110],"<?(*,,...,x":[112],")3y3y":[114],"^(*i>":[116],">*m)":[117],"3y":[118],"V":[121],"?(\u039b;":[122],"1":[123,215],".":[125,126],"(Henkin":[135],"used":[136],"x(":[137],"~^y":[138],"^)y":[139],"place":[141],"our":[143],"antecedents":[144],"#j,":[145],"but":[146,173],"since":[147],"A":[148],"3":[149,151],".B":[150],"C":[152],"fl":[154],"d":[155],"^DC^^^.BDC":[156],"are":[157,261,286,290,308],"equivalent":[158],"forms":[159],"any":[161],"containing":[163],"Al-2,":[164],"we":[165,174],"use":[166],"shorter":[168],"expression.)<pis":[169],"function":[171],"symbol,":[172],"shall":[175],"usually":[176],"refrain":[177],"from":[178],"indicating":[179],"its":[180],"argument":[181],"places,":[182],"this":[184,221,315],"should":[185],"not":[186,305],"cause":[187],"confusion.L'Abbe":[188],"[2]":[190],"showed":[191],"that":[192,271,285],"only":[193],"independence":[195],"A3":[197,211,240],"ever":[199],"doubt.We":[201],"here":[202],"show":[203],"general":[205],"(necessary":[206],"sufficient)":[208],"conditions":[209],"be":[213],"independent":[214,296],"method":[218],"determining":[220],"being":[222],"simple":[223],"inspection":[224],"truth-table":[227],"\u03a8":[229,254,284,303],".The":[230],"term":[231],"'Tarskian'":[232],"ensuing":[235],"theorem":[236],"chosen":[238],"because":[239],"often":[243],"so-called":[244],"Law":[245],"Tarski":[247],"with":[248],"commuted":[249],"antecedents.Def.":[250],"\u00a3":[251],"For":[252],"all":[253,281],"Tarskian":[258],"iff":[259,302],"there":[260],"valuations":[262],"say":[266],"\u03b2,":[269,279],"such":[270],"\u03b1,":[276],"arguments":[282],"\u03b2":[289],".THEOREM.A3":[294],"[Al-3,":[300],"(<?)\u2022}":[301],"Tarskian.1":[306],"We":[307],"indebted":[309],"Professor":[311],"Henkin":[312],"suggesting":[314],"problem.":[316]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}