{"id":"https://openalex.org/W2085536555","doi":"https://doi.org/10.1017/s0022481200051756","title":"Probabilities on finite models","display_name":"Probabilities on finite models","publication_year":1976,"publication_date":"1976-03-01","ids":{"openalex":"https://openalex.org/W2085536555","doi":"https://doi.org/10.1017/s0022481200051756","mag":"2085536555"},"language":"en","primary_location":{"id":"doi:10.1017/s0022481200051756","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0022481200051756","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/A5027117465","display_name":"Ronald Fagin","orcid":"https://orcid.org/0000-0002-7374-0347"},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ronald Fagin","raw_affiliation_strings":["Ibm Research Laboratory, San Jose, California 95193","IBM Research Laboratory, San Jose, California 95193"],"affiliations":[{"raw_affiliation_string":"Ibm Research Laboratory, San Jose, California 95193","institution_ids":["https://openalex.org/I1341412227"]},{"raw_affiliation_string":"IBM Research Laboratory, San Jose, California 95193","institution_ids":["https://openalex.org/I1341412227"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5027117465"],"corresponding_institution_ids":["https://openalex.org/I1341412227"],"apc_list":null,"apc_paid":null,"fwci":5.7413,"has_fulltext":false,"cited_by_count":334,"citation_normalized_percentile":{"value":0.95473152,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":100},"biblio":{"volume":"41","issue":"1","first_page":"50","last_page":"58"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9699000120162964,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9699000120162964,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9589999914169312,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8000575304031372},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6698602437973022},{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.629802405834198},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.6178256869316101},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.5916421413421631},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.5195025205612183},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.5040875673294067},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5027258396148682},{"id":"https://openalex.org/keywords/sentence","display_name":"Sentence","score":0.4921490550041199},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4667409062385559},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09115639328956604},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07695305347442627},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07619425654411316}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8000575304031372},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6698602437973022},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.629802405834198},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.6178256869316101},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.5916421413421631},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.5195025205612183},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.5040875673294067},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5027258396148682},{"id":"https://openalex.org/C2777530160","wikidata":"https://www.wikidata.org/wiki/Q41796","display_name":"Sentence","level":2,"score":0.4921490550041199},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4667409062385559},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09115639328956604},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07695305347442627},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07619425654411316},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0022481200051756","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0022481200051756","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/1183739716","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183739716","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":11,"referenced_works":["https://openalex.org/W1571008965","https://openalex.org/W1974159979","https://openalex.org/W2065143293","https://openalex.org/W2083716186","https://openalex.org/W2105269776","https://openalex.org/W2136111664","https://openalex.org/W2217170985","https://openalex.org/W2751862591","https://openalex.org/W3028000971","https://openalex.org/W3118259273","https://openalex.org/W6828599750"],"related_works":["https://openalex.org/W2951376487","https://openalex.org/W2171296020","https://openalex.org/W2901423989","https://openalex.org/W2132038253","https://openalex.org/W2941284322","https://openalex.org/W1982997203","https://openalex.org/W2883856176","https://openalex.org/W3013412531","https://openalex.org/W2172111502","https://openalex.org/W2157435664"],"abstract_inverted_index":{"Let":[0,20,181],"be":[1,21,44,144,182,206],"a":[2,14,85,128,140,168,183,213],"finite":[3,123,129,150],"set":[4,23,89,146],"of":[5,24,47,49,75,90,125,139,147,149,152,185,209,211,219,224,227,272],"(nonlogical)":[6],"predicate":[7,263],"symbols.":[8],"By":[9,216],"an":[10,220],"-structure,":[11],"we":[12,99,135,234],"mean":[13],"relational":[15],"structure":[16,193],"appropriate":[17],"for":[18,50,102,158,188],".":[19,196],"the":[22,45,73,137,145,207,225,270],"all":[25],"-structures":[26],"with":[27],"universe":[28],"{1,":[29],"\u2026,":[30],"n":[31,42,59,68,108,111,204,238,242,248,250,254,256],"}.":[32],"For":[33,197],"each":[34,103,122,159,189,198],"first-order":[35,91,104,160,199],"-sentence":[36,105,161,200],"\u03c3":[37,52,142,164,174],"(with":[38],"equality),":[39],"let":[40,202],"\u03bc":[41,58,107,255],"(\u03c3)":[43,60,109,205,239,251],"fraction":[46,208],"members":[48,210],"which":[51,186,212,265],"is":[53,77,84,120,156,177,214,266,274],"true.":[54,215],"We":[55],"show":[56,100,235],"that":[57,72,121,157,236,246],"always":[61],"converges":[62,240],"to":[63,143,195],"0":[64],"or":[65,165,175],"1":[66,112],"as":[67,241],"\u2192":[69,110,243],"\u221e,":[70,244],"and":[71,228,245],"rate":[74,271],"convergence":[76,273],"geometrically":[78,275],"fast.":[79,276],"In":[80],"fact,":[81,172],"if":[82],"T":[83,114,126],"certain":[86],"complete,":[87],"consistent":[88],"-sentences":[92],"introduced":[93],"by":[94,229],"H.":[95,132],"Gaifman":[96],"[6],":[97],"then":[98,269],"that,":[101],"\u03c3,":[106,201],"iff":[113],"\u22a9":[115],"\u03c9.":[116],"A":[117],"surprising":[118],"corollary":[119,155],"subset":[124,184],"has":[127,167],"model.":[130],"Following":[131],"Scholz":[133],"[8],":[134],"define":[136],"spectrum":[138,170],"sentence":[141],"cardinalities":[148],"models":[151],"\u03c3.":[153],"Another":[154],"a,":[162],"either":[163,173],"\u02dc\u03c3":[166,176],"cofinite":[169],"(in":[171],"\u201cnearly":[178],"always\u201c":[179],"true).":[180],"contains":[187,259],"in":[190],"exactly":[191],"one":[192,262],"isomorphic":[194],"\u03bd":[203,249],"making":[217],"use":[218],"asymptotic":[221],"estimate":[222],"[3]":[223],"cardinality":[226],"our":[230],"previously":[231],"mentioned":[232],"results,":[233],"v":[237],"lim":[247,253],"=":[252],"(\u03c3).":[257],"If":[258],"at":[260],"least":[261],"symbol":[264],"not":[267],"unary,":[268]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":12},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":10}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}