{"id":"https://openalex.org/W2159337272","doi":"https://doi.org/10.2307/2275786","title":"The hierarchy theorem for generalized quantifiers","display_name":"The hierarchy theorem for generalized quantifiers","publication_year":1996,"publication_date":"1996-09-01","ids":{"openalex":"https://openalex.org/W2159337272","doi":"https://doi.org/10.2307/2275786","mag":"2159337272"},"language":"en","primary_location":{"id":"doi:10.2307/2275786","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275786","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/A5078573449","display_name":"Lauri Hella","orcid":"https://orcid.org/0000-0002-9117-8124"},"institutions":[{"id":"https://openalex.org/I175532246","display_name":"University of Eastern Finland","ror":"https://ror.org/00cyydd11","country_code":"FI","type":"education","lineage":["https://openalex.org/I175532246"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Lauri Hella","raw_affiliation_strings":["Department of Mathematics, P.O. Box 4 (Yliopistonkatu 5), 00014University of Helsinki, Finland, E-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, P.O. Box 4 (Yliopistonkatu 5), 00014University of Helsinki, Finland, E-mail:","institution_ids":["https://openalex.org/I175532246"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031424171","display_name":"Kerkko Luosto","orcid":"https://orcid.org/0009-0007-3911-766X"},"institutions":[{"id":"https://openalex.org/I175532246","display_name":"University of Eastern Finland","ror":"https://ror.org/00cyydd11","country_code":"FI","type":"education","lineage":["https://openalex.org/I175532246"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Kerkko Luosto","raw_affiliation_strings":["Department of Mathematics, P.O. Box 4 (Yliopistonkatu 5), 00014University of Helsinki, Finland, E-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, P.O. Box 4 (Yliopistonkatu 5), 00014University of Helsinki, Finland, E-mail:","institution_ids":["https://openalex.org/I175532246"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067128079","display_name":"Jouko V\u00e4\u00e4n\u00e1nen","orcid":"https://orcid.org/0000-0003-4356-7974"},"institutions":[{"id":"https://openalex.org/I175532246","display_name":"University of Eastern Finland","ror":"https://ror.org/00cyydd11","country_code":"FI","type":"education","lineage":["https://openalex.org/I175532246"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Jouko V\u00e4\u00e4n\u00e4nen","raw_affiliation_strings":["Department of Mathematics, P.O. Box 4 (Yliopistonkatu 5), 00014University of Helsinki, Finland, E-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, P.O. Box 4 (Yliopistonkatu 5), 00014University of Helsinki, Finland, E-mail:","institution_ids":["https://openalex.org/I175532246"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078573449"],"corresponding_institution_ids":["https://openalex.org/I175532246"],"apc_list":null,"apc_paid":null,"fwci":3.0925,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.92226021,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"61","issue":"3","first_page":"802","last_page":"817"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9922999739646912,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9922999739646912,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9900000095367432,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9718000292778015,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.8337595462799072},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7838327288627625},{"id":"https://openalex.org/keywords/quantifier","display_name":"Quantifier (linguistics)","score":0.751819372177124},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.6382601261138916},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6113148927688599},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.5261670351028442},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4794555902481079},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4490011930465698},{"id":"https://openalex.org/keywords/order-type","display_name":"Order type","score":0.43238192796707153},{"id":"https://openalex.org/keywords/argument","display_name":"Argument (complex analysis)","score":0.4217297434806824},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32619136571884155},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13623806834220886},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13003170490264893}],"concepts":[{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.8337595462799072},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7838327288627625},{"id":"https://openalex.org/C2778523021","wikidata":"https://www.wikidata.org/wiki/Q5532504","display_name":"Quantifier (linguistics)","level":2,"score":0.751819372177124},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.6382601261138916},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6113148927688599},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.5261670351028442},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4794555902481079},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4490011930465698},{"id":"https://openalex.org/C138890893","wikidata":"https://www.wikidata.org/wiki/Q620006","display_name":"Order type","level":2,"score":0.43238192796707153},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.4217297434806824},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32619136571884155},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13623806834220886},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13003170490264893},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","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},{"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2307/2275786","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275786","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/1183745078","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183745078","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.38.9704","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.38.9704","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://mat-80.pc.helsinki.fi/pub/jvaahlv1.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4000000059604645,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W51954198","https://openalex.org/W124060014","https://openalex.org/W167076905","https://openalex.org/W251225716","https://openalex.org/W1499479569","https://openalex.org/W1516477821","https://openalex.org/W1894586384","https://openalex.org/W1974159979","https://openalex.org/W2002566654","https://openalex.org/W2003017965","https://openalex.org/W2026347847","https://openalex.org/W2031411912","https://openalex.org/W2038222783","https://openalex.org/W2076662767","https://openalex.org/W2112863615","https://openalex.org/W2181072414","https://openalex.org/W2498473121","https://openalex.org/W2911599249","https://openalex.org/W4230855714"],"related_works":["https://openalex.org/W2888918612","https://openalex.org/W2166285859","https://openalex.org/W3148597776","https://openalex.org/W2060412688","https://openalex.org/W1538206641","https://openalex.org/W80734134","https://openalex.org/W4300818667","https://openalex.org/W2273515602","https://openalex.org/W2016122306","https://openalex.org/W2187310579"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"concept":[2],"of":[3,7,32,47,57,65],"a":[4,8,44,83],"generalized":[5,33,45,63],"quantifier":[6,46],"given":[9],"similarity":[10,25,39,76,92],"type":[11,40,48,66],"was":[12,72],"defined":[13],"in":[14,54],"[12].":[15],"Our":[16],"main":[17],"result":[18],"says":[19],"that":[20],"on":[21],"finite":[22],"structures":[23],"different":[24,30],"types":[26,77],"give":[27],"rise":[28],"to":[29,90],"classes":[31],"quantifiers.":[34],"More":[35],"exactly,":[36],"for":[37,74],"every":[38],"t":[41,49,69],"there":[42],"is":[43,51],"which":[50],"not":[52],"definable":[53],"the":[55],"extension":[56],"first":[58],"order":[59],"logic":[60],"by":[61,78],"all":[62],"quantifiers":[64],"smaller":[67],"than":[68],".":[70],"This":[71],"proved":[73],"unary":[75],"Per":[79],"Lindstr\u00f6m":[80],"[17]":[81],"with":[82],"counting":[84],"argument.":[85],"We":[86],"extend":[87],"his":[88],"method":[89],"arbitrary":[91],"types.":[93]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}