{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,11]],"date-time":"2025-07-11T10:24:03Z","timestamp":1752229443031},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":6401,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1996,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The concept of a generalized quantifier of a given similarity type was defined in [12]. Our main result says that on finite structures different similarity types give rise to different classes of generalized quantifiers. More exactly, for every similarity type<jats:italic>t<\/jats:italic>there is a generalized quantifier of type<jats:italic>t<\/jats:italic>which is not definable in the extension of first order logic by all generalized quantifiers of type smaller than<jats:italic>t<\/jats:italic>. This was proved for unary similarity types by Per Lindstr\u00f6m [17] with a counting argument. We extend his method to arbitrary similarity types.<\/jats:p>","DOI":"10.2307\/2275786","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:59:03Z","timestamp":1146956343000},"page":"802-817","source":"Crossref","is-referenced-by-count":14,"title":["The hierarchy theorem for generalized quantifiers"],"prefix":"10.1017","volume":"61","author":[{"given":"Lauri","family":"Hella","sequence":"first","affiliation":[]},{"given":"Kerkko","family":"Luosto","sequence":"additional","affiliation":[]},{"given":"Jouko","family":"V\u00e4\u00e4n\u00e4nen","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200017138_ref009","unstructured":"Hella L. , V\u00e4\u00e4n\u00e4nen J. , and Westerst\u00e5hl D. , Definability ofpolyadic lifts of generalized quantifiers, to appear."},{"key":"S0022481200017138_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(89)90070-5"},{"key":"S0022481200017138_ref006","volume-title":"Information and Computation","author":"Hella","year":"1992"},{"key":"S0022481200017138_ref003","first-page":"83","volume-title":"Mathematical logic in Latin America","author":"Caicedo","year":"1980"},{"key":"S0022481200017138_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/BF01305232"},{"key":"S0022481200017138_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-0524-0_4"},{"key":"S0022481200017138_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(77)90116-9"},{"key":"S0022481200017138_ref014","volume-title":"Comment. 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Carol.","author":"Ne\u0161et\u0159il"},{"key":"S0022481200017138_ref016","first-page":"317","volume-title":"Logic and abstraction","volume":"1","author":"V\u00e4\u00e4n\u00e4nen","year":"1986"},{"key":"S0022481200017138_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)00025-X"},{"key":"S0022481200017138_ref013","unstructured":"Luosto K. , Hierarchies of monadic generalized quantifiers, to appear."},{"key":"S0022481200017138_ref015","first-page":"117","volume-title":"Set theory and hierarchy theory","volume":"14","author":"V\u00e4\u00e4n\u00e4nen","year":"1977"},{"key":"S0022481200017138_ref017","unstructured":"Westerst\u00e5hl D. , personal communication."},{"key":"S0022481200017138_ref018","first-page":"1","volume-title":"Handbook of philosophical logic","volume":"IV","author":"V\u00e4\u00e4n\u00e4nen","year":"1989"},{"key":"S0022481200017138_ref019","first-page":"173","volume-title":"Dynamics, polarity and quantification","author":"V\u00e4\u00e4n\u00e4nen","year":"1994"},{"key":"S0022481200017138_ref001","volume-title":"Model-theoretic logics","author":"Barwise","year":"1985"},{"key":"S0022481200017138_ref004","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/5.2.213"},{"key":"S0022481200017138_ref011","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093870519"},{"key":"S0022481200017138_ref012","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1111\/j.1755-2567.1966.tb00600.x","article-title":"First order predicate logic with generalized quantifiers","volume":"32","author":"Lindstr\u00f6m","year":"1966","journal-title":"Theoria"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200017138","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,4]],"date-time":"2024-02-04T07:28:47Z","timestamp":1707031727000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200017138\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,9]]},"references-count":19,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1996,9]]}},"alternative-id":["S0022481200017138"],"URL":"https:\/\/doi.org\/10.2307\/2275786","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,9]]}}}