Journal of Symbolic Logic

The Hierarchy Theorem for Generalized Quantifiers

Lauri Hella, Kerkko Luosto, and Jouko Vaananen

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745078

Mathematical Reviews number (MathSciNet)
MR1412511

Zentralblatt MATH identifier
0864.03028

JSTOR
links.jstor.org

Keywords
generalized quantifier finite model theory abstact model theory

Citation

Hella, Lauri; Luosto, Kerkko; Vaananen, Jouko. The Hierarchy Theorem for Generalized Quantifiers. J. Symbolic Logic 61 (1996), no. 3, 802--817. https://projecteuclid.org/euclid.jsl/1183745078


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