{"id":"https://openalex.org/W2134384958","doi":"https://doi.org/10.2307/2274015","title":"Completeness theorem for biprobability models","display_name":"Completeness theorem for biprobability models","publication_year":1986,"publication_date":"1986-09-01","ids":{"openalex":"https://openalex.org/W2134384958","doi":"https://doi.org/10.2307/2274015","mag":"2134384958"},"language":"en","primary_location":{"id":"doi:10.2307/2274015","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274015","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic 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/A5057630815","display_name":"Miodrag Ra\u0161kovi\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I14245010","display_name":"University of Kragujevac","ror":"https://ror.org/04f7vj627","country_code":"RS","type":"education","lineage":["https://openalex.org/I14245010"]}],"countries":["RS"],"is_corresponding":true,"raw_author_name":"Miodrag D. Ra\u0161kovi\u0107","raw_affiliation_strings":["Faculty of Science, University of Kragujevac, 34000 Kragujevac, Yugoslavia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Science, University of Kragujevac, 34000 Kragujevac, Yugoslavia","institution_ids":["https://openalex.org/I14245010"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057630815"],"corresponding_institution_ids":["https://openalex.org/I14245010"],"apc_list":null,"apc_paid":null,"fwci":0.5283,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.65082013,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"51","issue":"3","first_page":"586","last_page":"590"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9995999932289124,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9995999932289124,"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":0.9919999837875366,"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"}},{"id":"https://openalex.org/T10778","display_name":"Philosophy and History of Science","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.804746150970459},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.781877875328064},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.6654071807861328},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.6478677988052368},{"id":"https://openalex.org/keywords/g\u00f6dels-completeness-theorem","display_name":"G\u00f6del's completeness theorem","score":0.6434260010719299},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.5980405807495117},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5633852481842041},{"id":"https://openalex.org/keywords/rule-of-inference","display_name":"Rule of inference","score":0.4182160496711731},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09978261590003967}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.804746150970459},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.781877875328064},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.6654071807861328},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.6478677988052368},{"id":"https://openalex.org/C200116569","wikidata":"https://www.wikidata.org/wiki/Q902052","display_name":"G\u00f6del's completeness theorem","level":2,"score":0.6434260010719299},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.5980405807495117},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5633852481842041},{"id":"https://openalex.org/C3746660","wikidata":"https://www.wikidata.org/wiki/Q1068763","display_name":"Rule of inference","level":2,"score":0.4182160496711731},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09978261590003967},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2274015","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274015","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183742157","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183742157","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W40029885","https://openalex.org/W4205973993","https://openalex.org/W4293117209"],"related_works":["https://openalex.org/W2169551167","https://openalex.org/W2369292347","https://openalex.org/W3111972484","https://openalex.org/W1994701759","https://openalex.org/W4214646115","https://openalex.org/W1588277780","https://openalex.org/W958050847","https://openalex.org/W4252539554","https://openalex.org/W2144352681","https://openalex.org/W2019382695"],"abstract_inverted_index":{"The":[0,32,42,108],"aim":[1],"of":[2,49,85,127,130,147,151,178,187,195],"the":[3,8,37,113,125,128,132,137,141,158,165,176,183],"paper":[4],"is":[5,34,45,58,70,92,124],"to":[6,36,97,131],"prove":[7],"completeness":[9],"theorem":[10],"for":[11,117],"biprobability":[12,56],"models.":[13],"This":[14],"also":[15],"solves":[16],"Keisler's":[17],"Problem":[18],"5.4":[19],"(see":[20],"[4]).":[21],"Let":[22],"be":[23],"a":[24,59,71],"countable":[25],"admissible":[26],"set":[27],"and":[28,52,76,140,145,171,200],"\u03c9":[29],"\u2208":[30,206],".":[31,41,107,189,191,193],"logic":[33,40],"similar":[35],"standard":[38],"probability":[39,50,86],"only":[43],"difference":[44],"that":[46,89,167],"two":[47,83],"types":[48,84],"quantifiers":[51,109],"are":[53,82,110,149],"allowed.":[54],"A":[55],"model":[57],"structure":[60,73],"(":[61],",":[62,65,79,100,152,180],"\u03bc":[63,66,77,80,90,98,102,105],"1":[64,78,91,103,170],"2":[67,81,99,106,173],")":[68],"where":[69,199],"classical":[72],"without":[74],"operations":[75],"measures":[87],"such":[88],"absolutely":[93],"continuous":[94],"with":[95,157,164,182],"respect":[96],"i.e.":[101,116],"\u226a":[104],"interpreted":[111],"in":[112,155],"natural":[114],"way,":[115],"i":[118],"=":[119,203],"1,":[120],"2.":[121],"(The":[122],"measure":[123],"restriction":[126],"completion":[129],"\u03c3":[133],"-algebra":[134],"generated":[135],"by":[136],"measurable":[138],"rectangles":[139],"diagonal":[142],"sets":[143],"Axioms":[144,186],"rules":[146],"inference":[148],"those":[150],"as":[153],"listed":[154],"[2]":[156],"axiom":[159],"B":[160],"4":[161],"from":[162],"[4],":[163],"remark":[166],"both":[168],"P":[169,172,179],"can":[174],"play":[175],"role":[177],"together":[181],"following":[184],"axioms:":[185],"continuity":[188,197],"1)":[190],"2)":[192],"Axiom":[194],"absolute":[196],":":[198,208],"\u03a6":[201,207],"n":[202,211],"{":[204],"\u03c6":[205,209],"has":[210],"free":[212],"variables}.":[213]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2013,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}