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  1. The Hierarchy Theorem for Generalized Quantifiers.Lauri Hella, Kerkko Luosto & Jouko Väänänen - 1996 - Journal of Symbolic Logic 61 (3):802-817.
    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 t there is a generalized quantifier of type t which is not definable in the extension of first order logic by all generalized quantifiers of type smaller than t. This was proved for unary similarity types by Per Lindström [17] with (...)
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  • Questions About Quantifiers.Johan van Benthem - 1984 - Journal of Symbolic Logic 49 (2):443-466.
  • Generalized Quantifiers and Pebble Games on Finite Structures.Phokion G. Kolaitis & Jouko A. Väänänen - 1995 - Annals of Pure and Applied Logic 74 (1):23-75.
    First-order logic is known to have a severely limited expressive power on finite structures. As a result, several different extensions have been investigated, including fragments of second-order logic, fixpoint logic, and the infinitary logic L∞ωω in which every formula has only a finite number of variables. In this paper, we study generalized quantifiers in the realm of finite structures and combine them with the infinitary logic L∞ωω to obtain the logics L∞ωω, where Q = {Qi: iε I} is a family (...)
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  • Unary Quantifiers on Finite Models.Jouko Väänänen - 1997 - Journal of Logic, Language and Information 6 (3):275-304.
    In this paper (except in Section 5) all quantifiers are assumedto be so called simple unaryquantifiers, and all models are assumedto be finite. We give a necessary and sufficientcondition for a quantifier to be definablein terms of monotone quantifiers. For amonotone quantifier we give a necessaryand sufficient condition for beingdefinable in terms of a given set of bounded monotonequantifiers. Finally, we give a necessaryand sufficient condition for a monotonequantifier to be definable in terms of agiven monotone quantifier.Our analysis shows that (...)
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  • Generalized Quantifiers and Natural Language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
  • Generalized Quantifiers and Natural Language.Jon Barwise - 1980 - Linguistics and Philosophy 4:159.
  • A Semantic Characterization of Natural Language Determiners.Edward L. Keenan & Jonathan Stavi - 1986 - Linguistics and Philosophy 9 (3):253 - 326.
  • Essays in Logical Semantics.Johan van Benthem - 1988 - Studia Logica 47 (2):172-173.
     
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  • Essays in Logical Semantics.J. F. A. K. van Benthem - 1986
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  • D. Westerstå Hl. Quantifiers in Formal and Natural Languages.E. L. Keenan - 1997 - In Benthem & Meulen (eds.), Handbook of Logic and Language. MIT Press. pp. 837--893.
     
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