{"id":"https://openalex.org/W2087424958","doi":"https://doi.org/10.2307/2273725","title":"Sheaves and Boolean valued model theory","display_name":"Sheaves and Boolean valued model theory","publication_year":1979,"publication_date":"1979-06-01","ids":{"openalex":"https://openalex.org/W2087424958","doi":"https://doi.org/10.2307/2273725","mag":"2087424958"},"language":"en","primary_location":{"id":"doi:10.2307/2273725","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273725","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/A5032041518","display_name":"George Loullis","orcid":null},"institutions":[{"id":"https://openalex.org/I177328695","display_name":"Union College","ror":"https://ror.org/058w5nk68","country_code":"US","type":"education","lineage":["https://openalex.org/I177328695"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"George Loullis","raw_affiliation_strings":["Union College, Schenectady, New York 12308"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Union College, Schenectady, New York 12308","institution_ids":["https://openalex.org/I177328695"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5032041518"],"corresponding_institution_ids":["https://openalex.org/I177328695"],"apc_list":null,"apc_paid":null,"fwci":3.2011,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.93946984,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"44","issue":"2","first_page":"153","last_page":"183"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10778","display_name":"Philosophy and History of Science","score":0.9696000218391418,"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"}},"topics":[{"id":"https://openalex.org/T10778","display_name":"Philosophy and History of Science","score":0.9696000218391418,"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"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9563999772071838,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9521999955177307,"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/topos-theory","display_name":"Topos theory","score":0.941002368927002},{"id":"https://openalex.org/keywords/sheaf","display_name":"Sheaf","score":0.8321465253829956},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7014495134353638},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4584900438785553},{"id":"https://openalex.org/keywords/category-theory","display_name":"Category theory","score":0.43976497650146484},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.42795297503471375},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.41025620698928833},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3206455111503601},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.1310836672782898},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.1065855622291565}],"concepts":[{"id":"https://openalex.org/C182141236","wikidata":"https://www.wikidata.org/wiki/Q2143621","display_name":"Topos theory","level":2,"score":0.941002368927002},{"id":"https://openalex.org/C4017995","wikidata":"https://www.wikidata.org/wiki/Q595298","display_name":"Sheaf","level":2,"score":0.8321465253829956},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7014495134353638},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4584900438785553},{"id":"https://openalex.org/C54884031","wikidata":"https://www.wikidata.org/wiki/Q217413","display_name":"Category theory","level":2,"score":0.43976497650146484},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.42795297503471375},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.41025620698928833},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3206455111503601},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.1310836672782898},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.1065855622291565},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2273725","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273725","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/1183740384","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183740384","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":9,"referenced_works":["https://openalex.org/W138331535","https://openalex.org/W185482465","https://openalex.org/W205098610","https://openalex.org/W650961564","https://openalex.org/W1542760485","https://openalex.org/W2021757832","https://openalex.org/W2042984937","https://openalex.org/W2043338717","https://openalex.org/W2088927856"],"related_works":["https://openalex.org/W4318769964","https://openalex.org/W3098749204","https://openalex.org/W1557945163","https://openalex.org/W2075513489","https://openalex.org/W2069898398","https://openalex.org/W2900918889","https://openalex.org/W1985139661","https://openalex.org/W2005973892","https://openalex.org/W3151815541","https://openalex.org/W2046475951"],"abstract_inverted_index":{"In":[0],"recent":[1],"years":[2],"model":[3,15,152,242],"theorists":[4],"have":[5,207],"been":[6],"studying":[7],"various":[8],"sheaf-theoretic":[9],"notions":[10],"as":[11,93,106,198],"they":[12],"apply":[13],"to":[14,28,156],"theory.":[16],"For":[17],"quite":[18],"a":[19,22,31,48,68,87,94,169,183,191,199,211,245],"while":[20],"however,":[21],"sheaf":[23,69,88],"of":[24,59,67,70,85,89,96,109,116,128,131,144,151,165,168,182,188,197,225,231,247],"structures":[25,71,90,97,232],"was":[26],"considered":[27],"be":[29,195,234],"just":[30,92],"local":[32],"homeomorphism":[33],"between":[34],"topological":[35,192],"spaces":[36],"such":[37,52],"that":[38,53,179,223],"each":[39],"stalk":[40],"S":[41],"x":[42],"=":[43],"p":[44],"\u22121":[45],"(x)":[46],"is":[47,160],"model-theoretic":[49,61,114,227],"structure":[50],"and":[51,78,237],"certain":[54],"maps":[55],"are":[56,72],"continuous.":[57],"Some":[58],"the":[60,73,83,126,129,142,149,161,166,177,186],"work":[62],"done":[63],"with":[64,176],"this":[65,119,140],"notion":[66,167],"papers":[74],"by":[75,240],"Carson":[76],"[2]":[77],"Macintyre":[79,221],"[7].":[80],"Soon":[81],"came":[82],"idea":[84,178],"considering":[86],"not":[91],"collection":[95],"glued":[98],"together":[99],"in":[100,118,138,210],"some":[101,107,224],"continuous":[102],"way,":[103],"but":[104],"rather":[105,162],"sort":[108],"generalized":[110,200,218],"structure.":[111],"A":[112,158],"significant":[113],"study":[115],"sheaves":[117,189,230],"new":[120],"sense":[121],"became":[122],"possible":[123],"only":[124],"after":[125],"development":[127],"theory":[130,243],"topoi.":[132],"As":[133],"F.W.":[134],"Lawvere":[135],"pointed":[136],"out":[137],"[6],":[139],"represents":[141],"advance":[143,150],"mathematics":[145],"(in":[146],"our":[147],"case":[148],"theory)":[153],"from":[154],"metaphysics":[155],"dialectics.":[157],"topos":[159,171,184,187,246],"ingenious":[163],"evolution":[164],"Grothendieck":[170],"[13].":[172],"It":[173],"provides":[174],"us":[175],"an":[180,208],"object":[181],"(e.g.":[185],"over":[190],"space)":[193],"may":[194,215,233],"thought":[196],"set.":[201],"Furthermore,":[202],"all":[203],"first-order":[204],"logical":[205],"operations":[206],"interpretation":[209],"topos,":[212],"hence":[213],"we":[214],"talk":[216],"about":[217,229],"structures.":[219],"Angus":[220],"suggested":[222],"his":[226],"results":[228],"understood":[235],"better":[236],"perhaps":[238],"simplified":[239],"doing":[241],"inside":[244],"sheaves.":[248]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}