{"id":"https://openalex.org/W1998344005","doi":"https://doi.org/10.1305/ndjfl/1093893789","title":"A note on independence.","display_name":"A note on independence.","publication_year":1969,"publication_date":"1969-10-01","ids":{"openalex":"https://openalex.org/W1998344005","doi":"https://doi.org/10.1305/ndjfl/1093893789","mag":"1998344005"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093893789","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093893789","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/A5077271335","display_name":"Anjan Shukla","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Anjan Shukla","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5077271335"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.15814687,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12752","display_name":"Global Peace and Security Dynamics","score":0.08070000261068344,"subfield":{"id":"https://openalex.org/subfields/3320","display_name":"Political Science and International Relations"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12752","display_name":"Global Peace and Security Dynamics","score":0.08070000261068344,"subfield":{"id":"https://openalex.org/subfields/3320","display_name":"Political Science and International Relations"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.6975189447402954},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4105174243450165},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.36764535307884216},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.33185267448425293},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3238706588745117},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1586180329322815},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.07637473940849304}],"concepts":[{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.6975189447402954},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4105174243450165},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.36764535307884216},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33185267448425293},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3238706588745117},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1586180329322815},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.07637473940849304},{"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/1093893789","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093893789","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/1093893789","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093893789","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":3,"referenced_works":["https://openalex.org/W2008165157","https://openalex.org/W2060658593","https://openalex.org/W2086723461"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"Acquaintance":[0],"with":[1],"[l]":[2],"is":[3,22],"presupposed":[4],"and":[5,78,92,99,103,115],"we":[6],"shall":[7],"use":[8],"its":[9],"numeration":[10],"of":[11,16,44,61,113,132],"the":[12,14,17,27,42,48,59,72,82,111,124,133,138],"axioms.At":[13],"end":[15],"paper":[18],"Thacher":[19],"Robinson":[20],"states:\"It":[21],"interesting":[23],"to":[24,109,129],"note":[25],"that":[26,31],"author":[28,49],"has":[29],"verified":[30],"no":[32],"normal":[33,52,68,105],"truth-table":[34,53,69],"in":[35,119,142],"<5":[36],"truth":[37],"values":[38,75],"will":[39],"suffice":[40],"for":[41,47,71],"independence":[43,60,112],"(2.2).Bernays":[45],"constructed":[46],"a":[50,120],"six-valued":[51,67,104],"(subsequently":[54],"lost)":[55],"which":[56],"also":[57,97],"shows":[58],"(2.2).\"The":[62],"following":[63],"(see":[64],"p.":[65],"411)":[66],"suffices":[70],"purpose.The":[73],"designated":[74],"are":[76,107,136],"0":[77],"1.":[79],"(2.2)":[80,116],"takes":[81],"value":[83],"2":[84],"if":[85],"p":[86],"=":[87,90,94],"0,":[88],"q":[89],"4":[91],"r":[93],"2.":[95],"See":[96],"[2]":[98],"[3]":[100],"where":[101],"five":[102],"truth-tables":[106],"used":[108,126],"establish":[110],"(2.1)":[114],"respectively":[117],"but":[118],"different":[121],"context,":[122],"i.e.,":[123],"connectives":[125],"besides":[127],"implication":[128],"obtain":[130],"formulations":[131],"propositional":[134],"calculus":[135],"not":[137],"same":[139],"as":[140],"those":[141],"[1].":[143]},"counts_by_year":[],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}
