Journal of Symbolic Logic

The Hierarchy Theorem for Generalized Quantifiers

Lauri Hella, Kerkko Luosto, and Jouko Vaananen

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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 Lindstrom [17] with a counting argument. We extend his method to arbitrary similarity types.

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J. Symbolic Logic, Volume 61, Issue 3 (1996), 802-817.

First available in Project Euclid: 6 July 2007

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generalized quantifier finite model theory abstact model theory


Hella, Lauri; Luosto, Kerkko; Vaananen, Jouko. The Hierarchy Theorem for Generalized Quantifiers. J. Symbolic Logic 61 (1996), no. 3, 802--817.

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