{"id":"https://openalex.org/W2077383316","doi":"https://doi.org/10.1305/ndjfl/1093957154","title":"On the infinity of positive logic.","display_name":"On the infinity of positive logic.","publication_year":1962,"publication_date":"1962-01-01","ids":{"openalex":"https://openalex.org/W2077383316","doi":"https://doi.org/10.1305/ndjfl/1093957154","mag":"2077383316"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093957154","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093957154","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":0.25203252,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"3","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.09839999675750732,"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":0.09839999675750732,"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":0.09380000084638596,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.09120000153779984,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.6259187459945679},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5415244102478027},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33061516284942627},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14789223670959473}],"concepts":[{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.6259187459945679},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5415244102478027},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33061516284942627},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14789223670959473}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1093957154","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093957154","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/1093957154","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093957154","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":0.46000000834465027,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2306553012","https://openalex.org/W4251417359","https://openalex.org/W1979597421","https://openalex.org/W2381059884","https://openalex.org/W4229993731","https://openalex.org/W2372756075","https://openalex.org/W1979193983","https://openalex.org/W2007980826","https://openalex.org/W2220405813","https://openalex.org/W4245490552"],"abstract_inverted_index":{"No":[0],"direct":[1],"proof":[2],"seems":[3],"to":[4,18,77,123,182],"have":[5,78],"been":[6],"published":[7],"of":[8,22,159,188],"the":[9,19,28,110,124,138,142,152,156,179,197],"theorem":[10],"that":[11,108,140],"no":[12,118,129],"finite":[13,119],"matrix":[14,107,120,158],"can":[15],"be":[16],"adequate":[17,122],"positive":[20,93,111,125,134,180],"logic":[21],"implication,":[23],"which":[24,163],"is":[25,76,90,121,131,135],"here":[26],"proved.In":[27],"alphabet":[29],"p":[30,32,47,66,84,183,192,195,201],"lf":[31],"2":[33],",":[34,39],".":[35,36,203],".,p":[37],"n":[38,75,89,115,130,133,150],"{n":[40],">":[41],"1),":[42],"form":[43],"(p":[44],"{":[45,193],"D":[46,50,65,194],"f":[48],")":[49],"p.":[51],"for":[52,68,128,162],"all":[53,69,79],"i,":[54],"/:":[55],"1":[56,71,154],"S":[57],"i":[58,73],"<":[59,72],"/":[60],"5s":[61],"n,":[62],"and":[63],"p^":[64],"x":[67,85,202],"i:":[70],"<n.A":[74],"these":[80],"expressions":[81],"as":[82,86],"antecedents,":[83],"consequent.Then":[87],"A":[88,114,132,149],"not":[91],"a":[92,186],"thesis":[94],"but":[95],"becomes":[96],"so":[97],"if":[98,141,166],"any":[99,104,167],"two":[100,168],"variables":[101,143,169],"are":[102,144,170],"identified.Hence":[103],"n-I":[105],"valued":[106,145],"validates":[109,113],"system,":[112],"\u00bb":[116],"Hence":[117],"system.Proof:":[126],"That":[127],"shown":[136],"by":[137,146],"fact":[139],"their":[147],"subscripts":[148],"has":[151],"value":[153],"in":[155,178],"infinite":[157],"Dummett's":[160],"LC":[161],"cf.":[164],"[l].While":[165],"identified,":[171],"there":[172],"results":[173],"either":[174],"an":[175],"antecedent":[176],"equivalent":[177],"system":[181],"l9":[184,196],"or":[185],"pair":[187],"antecedents":[189],"\u03c1":[190],"{y":[191],"consequent":[198],"being":[199],"always":[200]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}