Hierarchies of monadic generalized quantifiers

Journal of Symbolic Logic 65 (3):1241-1263 (2000)
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A combinatorial criterium is given when a monadic quantifier is expressible by means of universe-independent monadic quantifiers of width n. It is proved that the corresponding hierarchy does not collapse. As an application, it is shown that the second resumption (or vectorization) of the Hartig quantifier is not definable by monadic quantifiers. The techniques rely on Ramsey theory



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Citations of this work

Definability of polyadic lifts of generalized quantifiers.Lauri Hella, Jouko Väänänen & Dag Westerståhl - 1997 - Journal of Logic, Language and Information 6 (3):305-335.
Unary quantifiers on finite models.Jouko Väänänen - 1997 - Journal of Logic, Language and Information 6 (3):275-304.
On vectorizations of unary generalized quantifiers.Kerkko Luosto - 2012 - Archive for Mathematical Logic 51 (3-4):241-255.

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References found in this work

Definability hierarchies of general quantifiers.Lauri Hella - 1989 - Annals of Pure and Applied Logic 43 (3):235.
Finite generation problem and n-ary quantifiers.Lauri Hella & Kerkko Luosto - 1995 - In M. Krynicki, M. Mostowski & L. Szczerba (eds.), Quantifiers: Logics, Models and Computation. Kluwer Academic Publishers. pp. 63--104.

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