{"id":"https://openalex.org/W2132277994","doi":"https://doi.org/10.2178/jsl/1245158092","title":"A geometric zero-one law","display_name":"A geometric zero-one law","publication_year":2009,"publication_date":"2009-06-16","ids":{"openalex":"https://openalex.org/W2132277994","doi":"https://doi.org/10.2178/jsl/1245158092","mag":"2132277994"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1245158092","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1245158092","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":"The 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/A5040912618","display_name":"Robert H. Gilman","orcid":"https://orcid.org/0000-0002-9037-0712"},"institutions":[{"id":"https://openalex.org/I108468826","display_name":"Stevens Institute of Technology","ror":"https://ror.org/02z43xh36","country_code":"US","type":"education","lineage":["https://openalex.org/I108468826"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Robert H. Gilman","raw_affiliation_strings":["Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, Nj 07030, USA, E-mail:","Stevens Inst of Tech"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, Nj 07030, USA, E-mail:","institution_ids":["https://openalex.org/I108468826"]},{"raw_affiliation_string":"Stevens Inst of Tech","institution_ids":["https://openalex.org/I108468826"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065430432","display_name":"Yuri Gurevich","orcid":"https://orcid.org/0000-0001-7808-9293"},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I4210164937","display_name":"Microsoft Research (United Kingdom)","ror":"https://ror.org/05k87vq12","country_code":"GB","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210164937"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Yuri Gurevich","raw_affiliation_strings":["Microsoft Research, One Microsoft Way, Redmond, Wa 98052, USA E-mail:"],"affiliations":[{"raw_affiliation_string":"Microsoft Research, One Microsoft Way, Redmond, Wa 98052, USA E-mail:","institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I4210164937"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039441575","display_name":"Alexei Miasnikov","orcid":"https://orcid.org/0009-0006-7271-0011"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Alexei Miasnikov","raw_affiliation_strings":["Department of Mathematics and Statistics, Mcgill University, Montreal, Quebec H3A 2K6, Canada, E-mail:","McGill University"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Mcgill University, Montreal, Quebec H3A 2K6, Canada, E-mail:","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"McGill University","institution_ids":["https://openalex.org/I5023651"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5040912618"],"corresponding_institution_ids":["https://openalex.org/I108468826"],"apc_list":null,"apc_paid":null,"fwci":0.3428,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.63202157,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"74","issue":"3","first_page":"929","last_page":"938"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9988999962806702,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9988999962806702,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9973000288009644,"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":0.7478705048561096},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.6708309054374695},{"id":"https://openalex.org/keywords/substructure","display_name":"Substructure","score":0.5984001755714417},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5882115364074707},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.569991946220398},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.542312502861023},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.4891510307788849},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4358581304550171},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.433404803276062},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40036147832870483},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.27762728929519653},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20743131637573242}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7478705048561096},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.6708309054374695},{"id":"https://openalex.org/C99679407","wikidata":"https://www.wikidata.org/wiki/Q56761637","display_name":"Substructure","level":2,"score":0.5984001755714417},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5882115364074707},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.569991946220398},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.542312502861023},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.4891510307788849},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4358581304550171},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.433404803276062},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40036147832870483},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27762728929519653},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20743131637573242},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1245158092","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1245158092","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":"The Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1245158092","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1245158092","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":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.6899999976158142}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W76753297","https://openalex.org/W1209114946","https://openalex.org/W1482193060","https://openalex.org/W1517150411","https://openalex.org/W2024244453","https://openalex.org/W2076048718","https://openalex.org/W2085536555","https://openalex.org/W2103528061","https://openalex.org/W2264894310","https://openalex.org/W2398967050","https://openalex.org/W4238030752","https://openalex.org/W6628136609","https://openalex.org/W6683617215","https://openalex.org/W6820414510"],"related_works":["https://openalex.org/W3153444835","https://openalex.org/W2153916713","https://openalex.org/W2023846184","https://openalex.org/W2703419385","https://openalex.org/W2329056228","https://openalex.org/W2284584236","https://openalex.org/W1979083399","https://openalex.org/W2344320748","https://openalex.org/W2374530195","https://openalex.org/W4235336878"],"abstract_inverted_index":{"Abstract":[0],"Each":[1],"relational":[2],"structure":[3],"X":[4,12,25,44,60,72,78,107,126],"has":[5,108],"an":[6,22],"associated":[7],"Gaifman":[8],"graph,":[9],"which":[10],"endows":[11],"with":[13],"the":[14,34,57,80,133,148,160],"properties":[15],"of":[16,24,36,49,59,71,82,84,125,132],"a":[17,109,142],"graph.":[18],"If":[19],"x":[20,31,40,76,88],"is":[21,45,61,116,129],"element":[23],",":[26,79],"let":[27],"B":[28,85],"n":[29,38,86,97],"(":[30,87],")":[32,89],"be":[33],"ball":[35],"radius":[37],"around":[39],".":[41,127],"Suppose":[42,100],"that":[43,144],"infinite,":[46],"connected":[47],"and":[48],"bounded":[50],"degree.":[51],"A":[52],"first-order":[53],"sentence":[54],"\u03d5":[55,91,115],"in":[56,141],"language":[58],"almost":[62],"surely":[63],"true":[64,118],"(resp.":[65,94],"a.s.":[66,117,120],"false)":[67],"for":[68,74,103,122],"finite":[69,105,123],"substructures":[70,83,124],"if":[73],"every":[75,104,114],"\u2208":[77],"fraction":[81],"satisfying":[90],"approaches":[92,98],"1":[93],"0)":[95],"as":[96],"infinity.":[99],"further":[101],"that,":[102],"substructure,":[106],"disjoint":[110],"isomorphic":[111],"substructure.":[112],"Then":[113],"or":[119],"false":[121],"This":[128],"one":[130],"form":[131,143],"geometric":[134,161],"zero-one":[135,162],"law.":[136,163],"We":[137],"formulate":[138],"it":[139],"also":[140],"does":[145],"not":[146],"mention":[147],"ambient":[149],"infinite":[150],"structure.":[151],"In":[152],"addition,":[153],"we":[154],"investigate":[155],"various":[156],"questions":[157],"related":[158],"to":[159]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
