{"id":"https://openalex.org/W1988272906","doi":"https://doi.org/10.2178/jsl/1082418529","title":"On first-order sentences without finite models","display_name":"On first-order sentences without finite models","publication_year":2004,"publication_date":"2004-06-01","ids":{"openalex":"https://openalex.org/W1988272906","doi":"https://doi.org/10.2178/jsl/1082418529","mag":"1988272906"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1082418529","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1082418529","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/A5022335201","display_name":"Marko Djordjevi\u0107","orcid":"https://orcid.org/0000-0002-2903-3119"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Marko Djordjevi\u0107","raw_affiliation_strings":["Department of Mathematics, University of Uppsala, Box 480, 75106 Uppsala, Sweden, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Uppsala, Box 480, 75106 Uppsala, Sweden, E-mail:","institution_ids":["https://openalex.org/I123387679"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022335201"],"corresponding_institution_ids":["https://openalex.org/I123387679"],"apc_list":null,"apc_paid":null,"fwci":0.4125,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.57479459,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"69","issue":"2","first_page":"329","last_page":"339"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9995999932289124,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9962000250816345,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9939000010490417,"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":0.7899008989334106},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6727454662322998},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5941872596740723},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5782563090324402},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5379785299301147},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.49835896492004395},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.48341214656829834},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.4802401661872864},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4627513885498047},{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.4481731951236725},{"id":"https://openalex.org/keywords/sentence","display_name":"Sentence","score":0.4441206753253937},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43946871161460876},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.4387318789958954},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.09394016861915588},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0838513970375061}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7899008989334106},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6727454662322998},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5941872596740723},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5782563090324402},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5379785299301147},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.49835896492004395},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.48341214656829834},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.4802401661872864},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4627513885498047},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.4481731951236725},{"id":"https://openalex.org/C2777530160","wikidata":"https://www.wikidata.org/wiki/Q41796","display_name":"Sentence","level":2,"score":0.4441206753253937},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43946871161460876},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.4387318789958954},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.09394016861915588},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0838513970375061},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1082418529","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1082418529","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/1082418529","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1082418529","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":12,"referenced_works":["https://openalex.org/W599815360","https://openalex.org/W1026721552","https://openalex.org/W1538292722","https://openalex.org/W1965045995","https://openalex.org/W2005659848","https://openalex.org/W2033619719","https://openalex.org/W2056789578","https://openalex.org/W2076723110","https://openalex.org/W2107867923","https://openalex.org/W2169702497","https://openalex.org/W2335659743","https://openalex.org/W4256751134"],"related_works":["https://openalex.org/W2888918612","https://openalex.org/W3019662020","https://openalex.org/W2054347355","https://openalex.org/W3172619790","https://openalex.org/W2085054174","https://openalex.org/W2035456572","https://openalex.org/W2621137221","https://openalex.org/W1672266275","https://openalex.org/W2059675826","https://openalex.org/W2898981230"],"abstract_inverted_index":{"We":[0],"will":[1,185],"mainly":[2],"be":[3],"concerned":[4],"with":[5,209],"a":[6,10,14,27,48,81,86,118,133,151,245],"result":[7,28],"which":[8,29,78,113],"refutes":[9],"stronger":[11],"variant":[12],"of":[13,16,37,57,66,202,288],"conjecture":[15],"Macpherson":[17],"about":[18],"finitely":[19,270],"axiomatizable":[20],"\u03c9":[21,33,238,253,265],"-categorical":[22,34,254],"theories.":[23],"Then":[24],"we":[25,61],"prove":[26],"implies":[30],"that":[31,80,94,102,115,155,165,196,231],"the":[32,42,64,171,180,187,214,221,242,274],"stable":[35],"pseudoplanes":[36],"Hrushovski":[38],"do":[39],"not":[40,145,237],"have":[41,186],"finite":[43,53,250],"submodel":[44],"property.":[45],"Let's":[46,194],"call":[47],"consistent":[49],"first-order":[50,76,111],"sentence":[51,77,112],"without":[52,249],"models":[54,251],"an":[55,200],"axiom":[56,201],"infinity":[58,203],".":[59,106,159,193,225,290],"Can":[60],"somehow":[62],"describe":[63],"axioms":[65],"infinity?":[67],"Two":[68],"standard":[69],"examples":[70],"are:":[71],"\u03d5":[72,107,166,232],"1":[73,167,277],":":[74,109],"A":[75,110],"expresses":[79,114],"binary":[82],"relation":[83],"<":[84,104,183,262,264],"on":[85],"nonempty":[87],"universe":[88],"is":[89,99,117,132,150,199,236,241,252],"transitive":[90],"and":[91,93,204,256],"irreflexive":[92],"for":[95,124,138,191,259],"every":[96,125,139,205,260],"x":[97,103,120,129,140,143,158,182,276,279],"there":[98,116,149,267],"y":[100,105,153,184],"such":[101,121,154,164,230],"2":[108,233],"unique":[119,152],"that,":[122],"(0)":[123,147],"y,":[126],"s(y)":[127,156],"\u2260":[128],"(where":[130],"s":[131],"unary":[134],"function":[135],"symbol),":[136],"and,":[137],",":[141,266,281],"if":[142,197,255],"does":[144],"satisfy":[146],"then":[148,218],"=":[157],"Every":[160,226],"complete":[161,206,227,246],"theory":[162,207,228,247],"T":[163,169,192,208,212,229,235,248,289],"\u03f5":[168,211,234],"has":[170,213,220],"strict":[172,188,215,222],"order":[173,189,216,223],"property":[174,190,224],"(as":[175],"defined":[176],"in":[177,273,285],"[10]),":[178],"since":[179],"formula":[181],"say":[195],"\u03a8":[198,210,219],"property,":[217],"-categorical.":[239],"This":[240],"case":[243],"because":[244],"only":[257,269],"if,":[258],"0":[261],"n":[263,280],"are":[268],"many":[271],"formulas":[272],"variables":[275],",\u2026,":[278],"up":[282],"to":[283],"equivalence,":[284],"any":[286],"model":[287]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}